Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Systems Using Linear Matrix Inequalities

Output Feedback Guaranteed Cost Control for Linear Uncertain System with Input Saturation

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

This paper investigates the problem of delay-dependent output feedback guaranteed cost controller design for uncertain discrete-time switched systems with time-varying state delay. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a switched dynamic output feedback controller guaranteeing the asymptotic stability of the resulting closed-loop system and minimizing a specified cost function. Based on a delay-dependent switched Lyapunov-Krasovskii functional (DDSLKF) combined with Finsler's Lemma, a novel delay-dependent robust performance analysis result is first proposed and in turn the output feedback controller synthesis is developed. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

This paper focuses on the problem of robust guaranteed cost control for a class of nonlinear systems described by the Takagi-Sugeno (T-S ) fuzzy descriptor model with time-varying delay and parameter uncertainties. The less conservative sufficient conditions for the existence of robust guaranteed cost controller via state feedback are given in terms of linear matrix inequalities (LMIs). And the design of optimal guaranteed cost controller can be reduced to a convex optimization problem. The designed controller not only guarantees the robust quadratic stability of the closed-loop system, but also provides a minimized 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.

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.

Distributed control architecture can bring many benefits to the engine control system, but the delay and packet dropout introduced by network communication will bring negative effects to the control system. The aging and deterioration of the engine are also obstacles in the design of the engine control system. This paper is concerned with the problem of guaranteed cost control for a distributed engine control system (DECS) with these negative constraints. Firstly, a model of DECS with multiple delays, packet dropouts and uncertainties is built. Secondly, a multiple delay-dependent guaranteed cost controller design method is proposed in the form of a set of linear matrix inequalities (LMIs). The non-convex optimal controller design problem is transformed into a convex optimization problem through the cone complementarity linearization (CCL) method, and the suboptimal controller is designed iteratively. Thirdly, turboshaft engine aging and deterioration are treated as sources of uncertainties, and the norm-bounded uncertain model of the turboshaft engine is modeled. Finally, the numerical simulations demonstrate the effectiveness and applicability of the guaranteed cost controller designed for DECS with multiple delays, packet dropouts, engine aging and deteriorations.

In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd.

This paper deals with the guaranteed cost control problem for a class of uncertain linear discrete-time switched systems with time-delay under arbitrary switching laws. The purpose 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. A sufficient condition on the existence of guaranteed cost controllers is derived based on Lyapunov theory together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

Guaranteed cost control problems for discrete-time systems with uncertainties and time delays are addressed in this paper. The delays may simultaneously appear not only in the state, but in control input and measurement output. Also, parametric uncertainties may exist in all system matrices of the systems considered in this paper. First, a new linear matrix inequality (LMI)-based approach is developed to construct dynamic guaranteed cost controllers for delay systems without uncertainties. Then this result is extended to discrete-time delay systems with uncertainties in linear fractional form in all system matrices. The solvability of these robust control problems for uncertain delay systems can be reduced to that for certain auxiliary systems without uncertainty. Numerical examples are provided to show the effectiveness of our approach.

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.

The linear Markov jump model that is usually used in the analysis and design phases is an approximation of a real nonlinear system with Markov jumps in the neighborhood of the operating point. For many reasons well known in the control community, the systems parameters and the operating point change with time and therefore, the fixed linear Markov jump model is not adequate to guarantee robustness of system performance. Besides this, the system can be affected by exogenous disturbances, which will make the degradation worse. To overcome this surprise, the control engineer should take care of these uncertainties and exogenous disturbances during the analysis and design phases to guarantee the required stability and other system performance, despite the presence of uncertainties in the system. The results presented so far for the class of linear systems with Markov jumps and time delay are not adequate to guarantee the robustness of the desired performance. The robust H∞ control problem was developed to maintain robustness of stability and performance when it known algorithms lack robustness, that is, the system parameters have uncertainties. This chapter deals with the robust H∞ control and the guaranteed cost control problems for jump linear systems with norm-bounded uncertainties and time delay. The rest of the chapter is organized as follows.we deal with the robust H∞ control problem. considers he guaranteed cost control problem. we cover the output feedback guaranteed cost control problem.

The problem of robust guaranteed cost control for a class of uncertain stochastic systems with Markov jump parameters subject to actuator saturation is discussed. The concept of domain of attraction is used to analyze the stochastic stability and a sufficient condition which guarantees the intersection of ellipsoid invariant set under different modes in the domain of attraction is presented. The solvability condition of robust guaranteed cost controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller such that the closed-loop system is stochastically stable and the cost function value is minimized. A numerical example is given to verify the effectiveness of this method.

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.