Problem Of Non-fragile Guaranteed Cost Control Research Articles

Non-fragile guaranteed cost control of nonlinear switched systems with actuator saturation

This paper considers a non-fragile guaranteed cost control problem for a class of nonlinear switched systems with actuator saturation. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization and the performance index of guaranteed cost control. To ensure the asymptotic stability of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and non-fragile state feedback controllers are designed using the multiple Lyapunov functions method. On this basis, an optimization problem is solved by adopting linear matrix inequality (LMI) constraints, and the minimum upper bound of cost function is determined. At the end of the paper, a numerical example is given to prove the effectiveness of the proposed method.

A generalized multiple Lyapunov functions method based non-fragile guaranteed cost control for uncertain switched fuzzy systems

This paper is concerned with a non-fragile guaranteed cost control problem for a class of uncertain switched fuzzy systems which are described by switched Takagi–Sugeno (T–S) fuzzy models. By employing the generalized multiple Lyapunov functions method, we present a sufficient condition to guarantee the closed-loop system asymptotically stable and possess an upper bound of the non-fragile guaranteed cost function. Meanwhile, a non-fragile state feedback control law and a switching law are designed. Moreover, an optimization problem, in which the minimal non-fragile guaranteed cost can be obtained, is solved. Finally, a simulation example is given to verify the feasibility and effectiveness of the proposed method.

NON-FRAGILE GUARANTEED COST CONTROL OF T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH LOCAL BILINEAR MODELS

This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bi- linear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.

Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input

Abstract This article considers non-fragile guaranteed cost control problem for a class of uncertain neutral system with time-varying delays in both state and control input. Delay-dependent criteria are proposed to guarantee the robust stabilization of systems. Linear matrix inequality (LMI) optimization approach is used to solve the non-fragile guaranteed cost control problem. Non-fragile guaranteed cost control for unperturbed neutral system is considered in the first step. Robust non-fragile guaranteed cost control for uncertain neutral system is designed directly from the unperturbed condition. An efficient approach is proposed to design the non-fragile guaranteed cost control for uncertain neutral systems. LMI toolbox of Matlab is used to implement the proposed results. Finally, a numerical example is illustrated to show the usefulness of the proposed results.

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.

On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays

In this article, the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation. The multiple time-varying delays are considered. The uncertainty is nonlinear time-varying and is bounded in magnitude. For all admissible uncertainties, time delays, and controller gain variations, the problem is to design a memoryless state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function. Several criteria for the existence of such controllers are derived using the Lyapunov method. A feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities. A numerical example is given to illustrate the proposed method.

Non-fragile guaranteed cost control of uncertain large-scale systems with time-varying delays

The robust non-fragile guaranteed cost control problem is studied in this paper for a class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.