• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.8
• /
• pp.1491-1497
• /
• 2007

This paper considers robust and non-fragile guaranteed cost controller design method for descriptor systems with parameter uncertainties and time delay, and static state feedback controller with gain variations. The existence condition of controller, the design method of controller, the upper bound to minimize guaranteed cost function, and the measure of non-fragility in controller are proposed using linear matrix inequality (LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile guaranteed cost controller guarantees the asymptotic stability and non-fragility of the closed loop systems in spite of parameter uncertainties, time delay, and controller fragility.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.5
• /
• pp.492-500
• /
• 2007

This paper focuses on the problem of guaranteed cost control for a class of uncertain linear delay systems with actuator failures. When actuators suffer "serious failure" the never failed actuators can not stabilize the system, based on switching strategy of average dwell time method, under the condition that activation time ratio between the system without actuator failure and the system with actuator failures is not less than a specified constant, a sufficient condition for exponential stability and weighted guaranteed cost performance are developed in terms of linear matrix inequalities (LMIs). Finally, as an example, a river pollution control problem illustrates the effectiveness of the proposed approach.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.2
• /
• pp.151-157
• /
• 2008

A non-fragile guaranteed cost control (GCC) problem is presented for a class of discrete time-delay nonlinear systems described by Takagi-Sugeno (T-S) fuzzy model. The systems are assumed to have norm-bounded time-varying uncertainties in the matrices of state, delayed state and control gains. Sufficient conditions are first obtained which guarantee that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Then the design method of the non-fragile guaranteed cost controller is formulated in terms of the linear matrix inequality (LMI) approach. A numerical example is given to illustrate the effectiveness of the proposed design method.

• 제어로봇시스템학회:학술대회논문집
• /
• 1986.10a
• /
• pp.367-369
• /
• 1986

Guaranteed cost control is a method applicable to a class of systems with uncertain parameters that guarantees an upper bound of the cost functional. This paper is concerned with a matrix decomposition technique used to yield a reasonable upper bound of the cost functional for a finite-time LQ regulator problem. The uncertain linear systems dealt with in this paper are described by a set of state equations of single-input phase-variable canonical form which contain unknown but bounded uncertain parameters.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.52 no.3
• /
• pp.129-133
• /
• 2003

In this paper, we consider the robust guaranteed cost control problem for a class of uncertain neutral systems with given quadratic cost functions. The uncertainty is assumed to be norm-bounded and time-varying. The goal in this study is to design the memoryless state feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound lot all admissible uncertainty. Some criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the Lyapunov second method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.61-76
• /
• 2002

The robust non-fragile guaranteed cost control problem is studied in this paper for 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-hounded arid 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 far 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 contrellers is 7iven in terms of the feasible solution to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.11 no.1
• /
• pp.606-623
• /
• 2019

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust $H_{\infty}$ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust $H_{\infty}$ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.44 no.1
• /
• pp.59-66
• /
• 2007

In this paper, we consider the non-fragile robust guaranteed cost state feedback controllers design method for descriptor systems with parameter uncertainties and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile robust guaranteed cost controller, the measure of non-fragility in controller, the upper bound of guaranteed cost performance measure to minimize the guaranteed cost are presented via LMI(linear matrix inequality) technique. Also, the sufficient condition can be rewritten as LMI form in terms of transformed variables through singular value decomposition, some changes of variables, and Schur complements. Therefore, the obtained non-fragile robust guaranteed cost controller satisfies the asymptotic stability and minimizes the guaranteed cost for the closed loop descriptor systems with parameter uncertainties and controller fragility. Finally, a numerical example is given to illustrate the design method.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.46 no.3
• /
• pp.15-21
• /
• 2009

In this paper, we consider the design problem of robust stabilization and robust guaranteed cost state feedback controller for discrete-time singular systems with parameter uncertainties by LMI(linear matrix inequality) approach without semi-definite condition and decomposition of system matrices. The objective of robust stabilization controller is to construct a state feedback controller such that the closed-loop system is regular, causal, and stable. In the case of robust guaranteed cost control, the optimal value of guaranteed cost and controller design method are presented on the basis of robust stabilization control technique. Finally, a numerical example is provided to show the validity of the design methods.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.51 no.11
• /
• pp.503-509
• /
• 2002

In this paper, the robust non-fragile guaranteed cost control problem is studied for a class of linear large-scale systems with uncertainties and a 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 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 and controller gain variations. 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.