Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system

This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.

Guaranteed cost sampled-data control for uncertain nonlinear time-varying delay system

The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].

Guaranteed Cost Control for Uncertain Nonlinear Time-Delay Neutral Systems Based on T-S Fuzzy Model

The problem of guaranteed cost fuzzy controller is studied for a class of nonlinear time-delay neutral sys-tems with norm-bounded uncertainty based on T-S model. The sufficient conditions are first derived for the existenceof guaranteed cost fuzzy controllers. These sufficient conditions are equivalent to a kind of linear matrix inequalities.Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteedcost controller.

Delay-dependent guaranteed cost control for uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays

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.

Guaranteed cost control for saturated uncertain linear systems

In this paper, we discuss the problem of guaranteed cost control for uncertain linear systems subject to actuator saturation. Based on the quadratic and non-quadratic Lyapunov functions, sufficient conditions for the robust stability and performance are derived. Moreover, all the conditions can be expressed as linear matrix inequalities （LMIs） or bilinear matrix inequalities （BMIs） in terms of the feedback gain. Thus, the static controller can be effectively synthesized via convex optimization. A numerical example illustrates the effectiveness of the method.

On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.

Guaranteed cost control for networked control systems

The guaranteed cost control problem for networked control systems (NCSs) is addressed under communication constraints and varying sampling rate. First of all, a simple information-scheduling scheme is presented to describe the scheduling approach of system signals in NCSs. Then, based on such a scheme and given sampling method, the design procedure in dynamic output feedback manner is also derived which renders the closed loop system to be asymptotically stable and guarantees an upper bound of the LQ performance cost function.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.

Guaranteed Cost Controller Design of Networked Control Systems with State Delay

这份报纸为联网的控制系统(NCS ) 的一个类涉及州反馈的保证费用控制器设计与州延期。NCS 的一个新模型在导致网络的延期的考虑下面被提供。为为 NCS 的一个保证费用控制器的存在的一个 suffcient 条件被一套线性矩阵不平等(LMI ) 介绍。一个方法，它能转变对非凸凸，被使用。因此，一个数字算法被建议获得更低的界限。通过一个例子的理论分析显示出方法的有效性。

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.

Optimal guaranteed cost control for fuzzy descriptor systems with time-varying delay

Based on the delay-independent rule, the problem of optimal guaranteed cost control for a class of Takagi-Sugeno （T-S） fuzzy descriptor systems with time-varying delay is studied. A linear quadratic cost function is considered as the performance index of the closed-loop system. Sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities （LMIs）, and the design of an optimal guaranteed cost controller can be reduced to a convex optimization problem. It is shown that the designed controller not only guarantees the asymptotic stability of the closed-loop fuzzy descriptor delay system, but also provides an optimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

Delay-dependent guaranteed cost control for uncertain systems with both state and input delays

This paper considers the guaranteed cost control problem for a class of uncertain linear systems with both state and input delays. By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors, we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities. Two examples are presented which show the effectiveness of our approach.

Non-fragile guaranteed cost control for uncertain neutral large-scale interconnected systems

This paper focuses on the problem of non-fragile decentralized guaranteed cost control for uncertain neutral large-scale interconnected systems with time-varying delays in state,control input and interconnections.A novel scheme,viewing the interconnections with time-varying delays as effective information but not disturbances,is developed.Based on Lyapunov stability theory,using various techniques of decomposing and magnifying matrices,a design method of the non-fragile decentralized guaranteed cost controller for unperturbed neutral large-scale interconnected systems is proposed and the guaranteed cost is presented.The further results are derived for the uncertain case from the criterion of unperturbed neutral large-scale interconnected systems.Finally,an illustrative example shows that the results are significantly better than the existing results in the literatures.

Guaranteed cost control for discrete-time networked control systems with random Markov delays

The guaranteed cost control for a class of uncertain discrete-time networked control systems with random delays is addressed. The sensor-to-controller （S-C） and contraller-to-actuator （C-A） random network-induced delays are modeled as two Markov chains. The focus is on the design of a two-mode-dependent guar- anteed cost controller, which depends on both the current S-C delay and the most recently available C-A delay. The resulting closed-loop systems are special jump linear systems. Sufficient conditions for existence of guaranteed cost controller and an upper bound of cost function are established based on stochastic Lyapunov-Krasovakii functions and linear matrix inequality （LMI） approach. A simulation example illustrates the effectiveness of the proposed method.

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control (RGCC) with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fault model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities (LMIs) approach, to minimize the upper bound of a quadratic cost function under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs’ magnitudes be guaranteed. Thus, with the above multi-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.

Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay

This paper considers the guaranteed cost control problem for a class of uncertain discrete T-S fuzzy systems with time delay and a given quadratic cost function. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequalities （LMI） approach by constructing a specific nonquadratic Lyapunov-Krasovskii functional and a nonlinear PDC-like control law. A convex optimization problem is also formulated to select the optimal guaranteed cost controller that minimizes the upper bound of the closed-loop cost function. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Robust guaranteed cost observer design for linear uncertain jump systems with state delays

This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay.The transition of the jumping parameters in systems is governed by a finite-state Markov process.Based on the stability theory in stochastic differential equations,a sufficient condition on the existence of the proposed robust guaranteed cost observer is derived.Robust guaranteed cost observers are designed in terms of a set of linear coupled matrix inequalities.A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observers.