In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achieve...In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.展开更多
The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentia...The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities(LMIs). A simulation example is presented to demonstrate the effectiveness of the proposed design approach.展开更多
In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention...In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention is focused on designing a memoryless state feedback control law such that the closed-loop system is robust stochastically stable and the closed-loop cost function value is not more than a specified upper bound,for all admissible uncertainties. The key features of the approach include the introduction of a new type of suitable stochastic Lyapunov functional and free weighting matrices techniques. Sufficient conditions for the existence of such controller are obtained in terms of a set of linear matrix inequalities. A numerical example is given to illustrate the less conservatism of the proposed techniques.展开更多
The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e....The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.展开更多
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions ...This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.展开更多
This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stabi...This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.展开更多
This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, ...This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities (LMIs). Numerical examples show the effectiveness of the proposed methods.展开更多
We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite...We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.展开更多
This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual g...This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual generator based on the filter of which its parameters matrices are dependent on the system mode, that is, the fault detection filter is a Markovian jump system as well. The design of fault detection filter is reduced to H-infinity filtering problem by using H-infinity control theory, which can guarantee the difference between the residual and the fault (or, more generally weighted fault) as small as possible in the context of enhancing the robustness of residual to modeling errors, control inputs and unknown inputs. Sufficient condition for the existence of the above filters is established by means of linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the feasibility of the proposed method.展开更多
This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Ma...This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.展开更多
The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. Th...The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.展开更多
In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained...In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.展开更多
The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new d...The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality (LMI), and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.展开更多
The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensure...The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.展开更多
In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that...In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.展开更多
This article discusses the synchronization problem of singular neutral complex dynamical networks(SNCDN)with distributed delay and Markovian jump parameters via pinning control.Pinning control strategies are designed ...This article discusses the synchronization problem of singular neutral complex dynamical networks(SNCDN)with distributed delay and Markovian jump parameters via pinning control.Pinning control strategies are designed to make the singular neutral complex networks synchronized.Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach.By applying the Lyapunov stability theory,Jensen's inequality,Schur complement,and linear matrix inequality technique,some new delay-dependent conditions are derived to guarantee the stability of the system.Finally,numerical examples are presented to illustrate the effectiveness of the obtained results.展开更多
基金Supported by National Natural Science Foundation of China(61174121, 61121003, 61203083) the Research Fund for the Doctoral Program of Higher Education of China Doctoral Foundation of University of Jinan (XBS1242)
基金supported by National Natural Science Foundation of China(61403254,61374039,61203143)Shanghai Pujiang Program(13PJ1406300)+2 种基金Natural Science Foundation of Shanghai City(13ZR1428500)Innovation Program of Shanghai Municipal Education Commission(14YZ083)Hujiang Foundation of China(C14002,B1402/D1402)
基金supported by the National Natural Science Foundation of China(61374073,61503356)Anhui Provincial Natural Science Foundation(1608085QF153)
文摘In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.
文摘The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities(LMIs). A simulation example is presented to demonstrate the effectiveness of the proposed design approach.
基金Sponsored by the National Defense Basic Research Foundation of China (Grant No. 9140A17030207HT01)
文摘In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention is focused on designing a memoryless state feedback control law such that the closed-loop system is robust stochastically stable and the closed-loop cost function value is not more than a specified upper bound,for all admissible uncertainties. The key features of the approach include the introduction of a new type of suitable stochastic Lyapunov functional and free weighting matrices techniques. Sufficient conditions for the existence of such controller are obtained in terms of a set of linear matrix inequalities. A numerical example is given to illustrate the less conservatism of the proposed techniques.
基金Postdoctoral Science Foundation of China (No. 20060400980)Postdoctoral Science Foundation of Shandong Province(No. 200603015)National Science Foundation of China (No. 10671112)
文摘The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.
基金This work was supported by the National Natural Science Foundation of China(No.60074007).
文摘This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.
文摘This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.
基金Supported by National High Technology Research and Development Program of China (863 Program) (2008AA042902), National Natural Science Foundation of P. R. China (60736021), and National Creative Research Groups Science Foundation of China (60721061)
基金supported by the National Creative Research Groups Science Foundation of China (No.60721062)the National High Technology Research and Development Program of China (863 Program) (2006AA04 Z182)the National Natural Science Foundation of China (No.60736021)
文摘This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities (LMIs). Numerical examples show the effectiveness of the proposed methods.
基金Project supported by Department of Science and Technology(DST)under research project No.SR/FTP/MS-039/2011
文摘We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.
基金the National Natural Science Foundation of China (No.60504008).
文摘This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual generator based on the filter of which its parameters matrices are dependent on the system mode, that is, the fault detection filter is a Markovian jump system as well. The design of fault detection filter is reduced to H-infinity filtering problem by using H-infinity control theory, which can guarantee the difference between the residual and the fault (or, more generally weighted fault) as small as possible in the context of enhancing the robustness of residual to modeling errors, control inputs and unknown inputs. Sufficient condition for the existence of the above filters is established by means of linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the feasibility of the proposed method.
文摘This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.
文摘The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
基金supported by NBHM project grant No.2/48(10)/2011-RD-II/865
文摘In this paper, global robust stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters is considered. A novel Linear matrix inequal- ity(LMI) based stability criterion is obtained to guarantee the asymptotic stability of uncertain stochastic recurrent neural networks with Markovian jumping parameters. The results are derived by using the Lyapunov functional technique, Lipchitz condition and S-procuture. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in [31] and [34] to show the effectiveness and conservativeness.
基金supported by the National Natural Science Foundation of China(60874114).
文摘The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with Maxkovian jumping parameters is considered. By applying Lyapunov functional method and Ito's differential rule, new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality (LMI), and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.
文摘The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.
基金Project supported by the National Natural Science Foundation of China (Grant No.60674026)the Jiangsu Provincial Natural Science Foundation of China (Grant No.BK2007016)
文摘In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.
基金The work of author was supported by NBHM grant.2/48(5)/2016/NBHMR.P)/-R-D II/14088。
文摘This article discusses the synchronization problem of singular neutral complex dynamical networks(SNCDN)with distributed delay and Markovian jump parameters via pinning control.Pinning control strategies are designed to make the singular neutral complex networks synchronized.Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach.By applying the Lyapunov stability theory,Jensen's inequality,Schur complement,and linear matrix inequality technique,some new delay-dependent conditions are derived to guarantee the stability of the system.Finally,numerical examples are presented to illustrate the effectiveness of the obtained results.