This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained u...This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions. Finally, the author shows that the usual weight functions based on nearest neighbor methods satisfy the designed assumptions imposed.展开更多
This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for ...The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.展开更多
In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, ...In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.展开更多
We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System (LIMAS) under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a...We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System (LIMAS) under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a general form, which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors. Secondly, a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem. Based on the partial stability theory, we derive a sufficient and necessary criterion of consensus convergence, which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols, and present an analytical formula of the consensus function. Lastly, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.展开更多
This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR(inverted pendulum type assistant robot). The motion equation is derived considering the non-holonomic constraint...This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR(inverted pendulum type assistant robot). The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator(LQR), linear quadratic Gaussian control(LQG), H_2 control and H_∞ control. Simulation is performed for all the approaches yielding good performance results.展开更多
In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive ob...In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.展开更多
In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertaintie...In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.展开更多
In order to reduce the resistance and improve the hydrodynamic performance of a ship, two hull form design methods are proposed based on the potential flow theory and viscous flow theory. The flow fields are meshed us...In order to reduce the resistance and improve the hydrodynamic performance of a ship, two hull form design methods are proposed based on the potential flow theory and viscous flow theory. The flow fields are meshed using body-fitted mesh and structured grids. The parameters of the hull modification function are the design variables. A three-dimensional modeling method is used to alter the geometry. The Non-Linear Programming(NLP) method is utilized to optimize a David Taylor Model Basin(DTMB) model 5415 ship under the constraints, including the displacement constraint. The optimization results show an effective reduction of the resistance. The two hull form design methods developed in this study can provide technical support and theoretical basis for designing green ships.展开更多
In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accu...In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.展开更多
For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method anal...For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is constructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.展开更多
In this paper, an Ethernet controller SoC solution and its low power design for testability (DFT) for information appliances are presented. On a single chip, an enhanced one-cycle 8-bit micro controller unit (MCU)...In this paper, an Ethernet controller SoC solution and its low power design for testability (DFT) for information appliances are presented. On a single chip, an enhanced one-cycle 8-bit micro controller unit (MCU), media access control (MAC) circuit and embedded memories such as static random access memory (SRAM), read only memory (ROM) and flash are all integrated together. In order to achieve high fault coverage, at the same time with low test power, different DFT techniques are adopted for different circuits: the scan circuit that reduces switching activity is implemented for digital logic circuits; BIST-based method is employed for the on-chip SRAM and ROM. According to the fault-modeling of embedded flash, we resort to a March-like method for flash built in self test (BIST). By all means above, the result shows that the fault coverage may reach 97%, and the SoC chip is implemented successfully by using 0.25 μm two-poly four-metal mixed signal complementary metal oxide semiconductor (CMOS) technology, the die area is 4.8×4.6 mm^2. Test results show that the maximum throughput of Ethemet packets may reach 7Mb·s^1.展开更多
The correlation between ground motion intensity measures (IM) and single-degree-of-freedom (SDOF) deformation demands is described in this study. Peak ground acceleration (APG), peak ground velocity (VPG), pea...The correlation between ground motion intensity measures (IM) and single-degree-of-freedom (SDOF) deformation demands is described in this study. Peak ground acceleration (APG), peak ground velocity (VPG), peak ground displacement (DPG), spectral acceleration at the first-mode period of vibration [As(T1)] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As(T1) or VPG and deformation demands. Furthermore, the effect of As(T1) and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.展开更多
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith...An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.展开更多
为解决基础隔震结构中隔震层位移需求过大的问题,提出了一种基础隔震结构(Base Isolated Structure,BIS)+串并联调谐质量阻尼器惯容器(Tuned Tandem Mass Damper-Inerter, TTMDI)的混合隔震体系。采用Bouc-Wen滞回模型模拟隔震层的非线...为解决基础隔震结构中隔震层位移需求过大的问题,提出了一种基础隔震结构(Base Isolated Structure,BIS)+串并联调谐质量阻尼器惯容器(Tuned Tandem Mass Damper-Inerter, TTMDI)的混合隔震体系。采用Bouc-Wen滞回模型模拟隔震层的非线性力-变形行为,基于随机等效线性化和模式搜索优化算法并考虑地震动模型,在频域内建立了BIS+TTMDI体系的优化设计框架。分别从鲁棒性、有效性、刚度和阻尼系数、冲程及对地震频率敏感性方面对BIS+TTMDI体系的性能进行评估,并与BIS+调谐质量阻尼器(Tuned Mass Damper, TMD)、串并联调谐质量阻尼器(TunedTandemMassDamper,TTMD)和调谐质量阻尼器惯容器(TunedMass Damper-Inerter, TMDI)进行比较。通过对近场地震动下某七层混合基础隔震结构(包括BIS+TTMDI和BIS+TMDI体系)的动力弹塑性分析,评价了其减/隔震性能。结果表明:BIS+TTMDI体系具有最好的减/隔震性能和强鲁棒性;而且在BIS+TTMDI体系中TTMDI的总阻尼需求不到BIS+TMDI体系中TMDI的一半,因而更为经济实用。展开更多
In order to improve the performance of linear time-varying(LTV)channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multipl...In order to improve the performance of linear time-varying(LTV)channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multiplexing(OFDM)system is proposed.Firstly,based on the compressive sensing theory,the average of the channel taps over one symbol duration in the LTV channel model is estimated.Secondly,in order to deal with the inter-carrier interference(ICI),the group-pilot design criterion is used based on the minimization of mutual coherence of the measurement.Finally,an efficient pilot pattern optimization algorithm is proposed by a dual layer loops iteration.The simulation results show that the new method uses less pilots,has a smaller bit error ratio(BER),and greater ability to deal with Doppler frequency shift than the traditional method does.展开更多
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable wit...This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.展开更多
基金This article was supported by the National Natural Science Foundation of China(10571001)the Innovation Group Foundation of Anhui University
文摘This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions. Finally, the author shows that the usual weight functions based on nearest neighbor methods satisfy the designed assumptions imposed.
基金the National Natural ScienceFoundation of China(19971001)
文摘This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
文摘The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.
文摘In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.
基金supported in part by NSF of China(61273006 and 6141101096)High Technology Research and Development Program of China(863Program)(2011AA110301)+2 种基金Specialized Research Fund for the Doctoral Program of Higher Education of China(20111103110017)St.Petersburg State University(9.38.674.2013)the Russian Foundation for Basic Research(13-01-00376-a and 15-58-53017)
文摘We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System (LIMAS) under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a general form, which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors. Secondly, a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem. Based on the partial stability theory, we derive a sufficient and necessary criterion of consensus convergence, which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols, and present an analytical formula of the consensus function. Lastly, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.
基金supported by the Deanship of Scientific Research(DSR)at the King Fahd University of Petroleum and Minerals(KFUPM)(141048)
文摘This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR(inverted pendulum type assistant robot). The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator(LQR), linear quadratic Gaussian control(LQG), H_2 control and H_∞ control. Simulation is performed for all the approaches yielding good performance results.
文摘In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.
文摘In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.
基金financially supported by the National P&D Program of China(Grant No.2016YFB0300700)the National Natural Science Foundation of China(Grant Nos.51779135 and 51009087)the Natural Science Foundation of Shanghai(Grant No.14ZR1419500)
文摘In order to reduce the resistance and improve the hydrodynamic performance of a ship, two hull form design methods are proposed based on the potential flow theory and viscous flow theory. The flow fields are meshed using body-fitted mesh and structured grids. The parameters of the hull modification function are the design variables. A three-dimensional modeling method is used to alter the geometry. The Non-Linear Programming(NLP) method is utilized to optimize a David Taylor Model Basin(DTMB) model 5415 ship under the constraints, including the displacement constraint. The optimization results show an effective reduction of the resistance. The two hull form design methods developed in this study can provide technical support and theoretical basis for designing green ships.
文摘In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.
基金supported by Program for New Century Excellent Talents in University, Ministry of Education of China (Grant No. NCET- 05-0285 )
文摘For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is constructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.
基金Supported by the National High Technology Research and Development Program of China (2006AA01Z226)
文摘In this paper, an Ethernet controller SoC solution and its low power design for testability (DFT) for information appliances are presented. On a single chip, an enhanced one-cycle 8-bit micro controller unit (MCU), media access control (MAC) circuit and embedded memories such as static random access memory (SRAM), read only memory (ROM) and flash are all integrated together. In order to achieve high fault coverage, at the same time with low test power, different DFT techniques are adopted for different circuits: the scan circuit that reduces switching activity is implemented for digital logic circuits; BIST-based method is employed for the on-chip SRAM and ROM. According to the fault-modeling of embedded flash, we resort to a March-like method for flash built in self test (BIST). By all means above, the result shows that the fault coverage may reach 97%, and the SoC chip is implemented successfully by using 0.25 μm two-poly four-metal mixed signal complementary metal oxide semiconductor (CMOS) technology, the die area is 4.8×4.6 mm^2. Test results show that the maximum throughput of Ethemet packets may reach 7Mb·s^1.
基金National Natural Science Foundation of China (50578007)
文摘The correlation between ground motion intensity measures (IM) and single-degree-of-freedom (SDOF) deformation demands is described in this study. Peak ground acceleration (APG), peak ground velocity (VPG), peak ground displacement (DPG), spectral acceleration at the first-mode period of vibration [As(T1)] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As(T1) or VPG and deformation demands. Furthermore, the effect of As(T1) and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
文摘An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.
文摘为解决基础隔震结构中隔震层位移需求过大的问题,提出了一种基础隔震结构(Base Isolated Structure,BIS)+串并联调谐质量阻尼器惯容器(Tuned Tandem Mass Damper-Inerter, TTMDI)的混合隔震体系。采用Bouc-Wen滞回模型模拟隔震层的非线性力-变形行为,基于随机等效线性化和模式搜索优化算法并考虑地震动模型,在频域内建立了BIS+TTMDI体系的优化设计框架。分别从鲁棒性、有效性、刚度和阻尼系数、冲程及对地震频率敏感性方面对BIS+TTMDI体系的性能进行评估,并与BIS+调谐质量阻尼器(Tuned Mass Damper, TMD)、串并联调谐质量阻尼器(TunedTandemMassDamper,TTMD)和调谐质量阻尼器惯容器(TunedMass Damper-Inerter, TMDI)进行比较。通过对近场地震动下某七层混合基础隔震结构(包括BIS+TTMDI和BIS+TMDI体系)的动力弹塑性分析,评价了其减/隔震性能。结果表明:BIS+TTMDI体系具有最好的减/隔震性能和强鲁棒性;而且在BIS+TTMDI体系中TTMDI的总阻尼需求不到BIS+TMDI体系中TMDI的一半,因而更为经济实用。
基金Supported by the National Natural Science Foundation of China(61571368)the Ministerial Level Advanced Research Foundation(950303HK,C9149C0511)
文摘In order to improve the performance of linear time-varying(LTV)channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multiplexing(OFDM)system is proposed.Firstly,based on the compressive sensing theory,the average of the channel taps over one symbol duration in the LTV channel model is estimated.Secondly,in order to deal with the inter-carrier interference(ICI),the group-pilot design criterion is used based on the minimization of mutual coherence of the measurement.Finally,an efficient pilot pattern optimization algorithm is proposed by a dual layer loops iteration.The simulation results show that the new method uses less pilots,has a smaller bit error ratio(BER),and greater ability to deal with Doppler frequency shift than the traditional method does.
文摘This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.