Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

Email: chlien{at}mail.nkmu.edu.tw Received on August 10, 2006; Accepted on September 6, 2006 In this paper, delay-dependent guaranteed cost observer-basedcontrol for neutral systems with time-varying delays is considered.Control and observer gains will be given from the linear matrixinequality feasible solutions. Optimal guaranteed cost observer-basedcontrol which will minimize the guaranteed cost of the systemis provided.     

Output-feedback guaranteed cost control for uncertain time-delay systems with Markov jumps

This paper considers the guaranteed cost control problem ofthe jump linear system with uncertain parameters and constanttime delay. The sufficient and necessary condition for the systemto be mean square quadratically stable (MSQS) is obtained. Usingthe LMI technique, an algorithm to design an output-feedbackguaranteed controller which stabilizes the system in the MSQSsense is developed.     

Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays

This paper deals with output feedback guaranteed cost control problem for a general class of uncertain linear discrete delay systems, where the state and the observation output are subjected to interval time-varying delay. The proposed output feedback controller uses the observation measurement to exponentially stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of augmented Lyapunov–Krasovskii functionals, a delay-dependent condition for the robust output feedback guaranteed cost control is established in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the efficiency of the proposed method.     

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.     

On the robustness of linear stabilizing feedback control for linear uncertain systems: Multi-input case

The robust stabilization of linear systems with constant uncertainties against structured perturbations using Lyapunov's theory is investigated. The only information needed on the uncertainties is the knowledge of their boundaries. The matching conditions of the uncertain systems are not required to be satisfied. It is first shown that, under some assumptions, the system can be transformed into a certain canonical controllable companion form. Then, under some additional assumptions, the existence of a linear controller which stabilizes the system based on Lyapunov's theory is shown.     

On guaranteed stability of uncertain linear systems via linear control

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.     

Delay-independent stabilization of uncertain linear systems of neutral type

In this paper, we show that a sufficient condition for the delay-independent stabilizability of linear delay systems, which had been obtained by Amemiya et al., is also valid for linear neutral systems with measurable state variables by a new differential-difference inequality.The authors express their appreciation to Professor G. Leitmann for his useful comments.     

On the robustness of linear stabilizing feedback control for linear uncertain systems

We investigate linear time-invariant scalar-input systems with constant uncertainties that are not required to satisfy matching conditions. In a previous paper, the existence of stabilizing discontinuous controllers is established under three assumptions for such systems. The first assumption requires controllability of the system for each uncertainty. The second is a condition on an uncertain Lyapunov equation, and the third is a boundedness condition related to the controllability matrix. In this paper, using the same assumptions, we show the existence of a linear stabilizing control. Our result is related to the high-gain theorem of classical control.     

Multiple delay-dependent guaranteed cost control for uncertain switched random nonlinear systems against intermittent sensor and actuator faults

In this paper, guaranteed cost control is investigated for switched random nonlinear systems against multiple state delays, model uncertainties, intermittent sensor and actuator faults. Other factors containing nonlinear dynamics, external disturbances as well as measurement noise are also considered. This is the first try to realize guaranteed cost control for uncertain switched random nonlinear systems against multiple time delays. In practice, color noise is more common than white noise in some specific situations. Thus, this paper considers random systems with color noise. In contrast to the previous study works, the suggested system can be applied to a wider range. First, a dynamic full-order output feedback controller is established to make the system stable. And an entire closed-loop system is got to achieve guaranteed cost control. Then, the multiple delay-dependent sufficient conditions are acquired through the piecewise Lyapunov function in the framework of linear matrix inequalities (LMIs). In the meantime, controller gain matrices are obtained. At last, two simulation examples are presented to verify the availability of the suggested approach.     

一类具有闭环极点约束的不确定线性系统的保性能控制

主要研究了闭环系统的极点约束在一个给定圆盘中的保性能控制问题,基于线性矩阵不等式处理方法给出了状态反馈控制器存在的充要条件,并利用线性矩阵不等式的解给出了保性能控制器的设计方法,得到一个状态反馈控制器,使得对所有允许的不确定性闭环系统稳定,并且闭环性能指标值不超过某个确定的上界.最后以数值例子验证了结果的正确性.     

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.     

Robust guaranteed cost control for discrete‐time systems via partially delay‐dependent controller with linear fractional uncertainties

In this article, a partially delay‐dependent controller is designed to analyze the guaranteed performance analysis of a class of uncertain discrete‐time systems with time‐varying delays. By constructing suitable Lyapunov–Krasovskii Functional (LKF), sufficient conditions are derived to ensure the system to be robustly stochastically stable in mean square sense by using Wirtinger‐based inequality and convex reciprocal lemma. The proper cost function is chosen to guarantee an adequate level of performance. The derived conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in MATLAB. Further, the advantage of employing the obtained results is illustrated via numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 113–122, 2016     

Switching design for suboptimal guaranteed cost control of 2-D nonlinear switched systems in the Roesser model

This paper deals with the problem of switching design for guaranteed cost control of discrete-time two-dimensional (2-D) nonlinear switched systems described by the Roesser model. The switching signal, which determines the active mode of the system, is subject to a state-dependent process whose values belong to a finite index set. By using 2-D common Lyapunov function approach, a sufficient condition expressed in terms of tractable matrix inequalities is first established to design a min-projection switching rule that makes the 2-D switched system asymptotically stable. The obtained result on stability analysis is then utilized to synthesize a suboptimal state feedback controller that minimizes the upper bound of a given infinite-horizon cost function. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.     

Static output feedback and guaranteed cost control of a class of discrete-time nonlinear systems with partial state measurements

In this paper both the static output feedback issue and the observer-based control of a class of discrete-time nonlinear systems are considered. Thanks to a newly developed linearization lemma, it is shown that the solution of the discrete-time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. An illustrative example is provided to show the usefulness of the proposed control designs.     

Optimal guaranteed control of linear systems under disturbances

This paper is devoted to the problem of the minimax control of a dynamical system with quadratic performance functional under external disturbances and geometric control constraints. The optimal guaranteed control strategy is obtained in explicit form.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 198–205, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-000771a.     

Asymptotic stability of differential systems of neutral type

We offer sufficient conditions for the asymptotic stability of the equilibrium point of linear neutral differential systems. An application of our results to a family of artificial neural networks of neutral type is also illustrated.     

Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems

In this article, the guaranteed cost control problem for a class of neutral delay systems is investigated. A linear--quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be solved easily by various efficient optimization algorithms.