Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

Abstract

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

“…The current results on the finite-time guaranteed cost control problem are focused on integer-order systems, [32][33][34][35][36][37] and few works are devoted to some kinds of fractional-order systems without time delays, [38][39][40][41] not mention to fractional-order systems with time-varying delays. The most frequently used method to solve the problem in these works, [32][33][34][35][36][37][38][39][40][41] the so-called Lyapunov-Krasovskii functional method, cannot be extended to uncertain fractional-order systems with interval time-varying delays easily. It is not easy to construct a suitable Lyapunov-Krasovskii functional for delayed fractional-order systems, and calculate its fractional derivative since the Leibniz rule does not hold for fractional derivatives.…”

“…Remark The current results on the finite‐time guaranteed cost control problem are focused on integer‐order systems, 32‐37 and few works are devoted to some kinds of fractional‐order systems without time delays, 38‐41 not mention to fractional‐order systems with time‐varying delays. The most frequently used method to solve the problem in these works, 32‐41 the so‐called Lyapunov–Krasovskii functional method, cannot be extended to uncertain fractional‐order systems with interval time‐varying delays easily. It is not easy to construct a suitable Lyapunov–Krasovskii functional for delayed fractional‐order systems, and calculate its fractional derivative since the Leibniz rule does not hold for fractional derivatives.…”

“…The problem of FTGCC is to find a feedback controller to finite‐time stabilize the system to guarantee an adequate cost level of performance. Following these ideas, Li et al 32 investigated the FTGCC of linear continuous‐time singular systems with norm‐bounded uncertainties. The problem of finite‐time $$$ {H}_{\infty } $$$ control for switched linear systems with time‐varying parametric perturbations was considered in Reference 33 based on a multiple event‐triggering strategies approach.…”

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

“…The GCC is an effective control method to improve and optimize system performance. Generally speaking, the goal of GCC is to design a proper controller such that the states (tracking errors) of the closed-loop system are bounded or asymptotically stable, and, most importantly, the corresponding cost function, which is often defined to make the system satisfying extra performance requirements except stability, is bounded by a known function (In this paper, for readability, the function is termed the upper bound of cost function (UBCF)) (Chang and Peng, 1972; Chen et al, 2004; Li et al, 2019; Senger and Trofino, 2016). At present, many relevant works have been reported (Boukas et al, 2003; Chen et al, 2003; Guo, 2002; Mai and Thanht, 2011; Niamsup and Phat, 2015; Park, 2004; Ren and Zhang, 2012; Xie and Tang, 2006; Zhang and Fang, 2008; Zhang et al, 2009).…”

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

“…During the past few decades have attracted much attention on singular systems that can describe various physical systems more directly and effectively than regular state-space systems (Feng and Shi, 2017a; Li et al, 2019; Xu and Lam, 2006; Zhang et al, 2017). Because the singular systems composed of a set of coupled differential equations (continuous systems)/or difference equations (discrete systems) and algebraic equations, the study of singular systems is more complicated than regular state-space systems (Dai, 1989).…”