This paper provides new stabilization criteria for a class of uncertain linear time-delay systems with saturating actuators for time-varying delays. Based on Lyapunov-Krasovskii functionals combined with LMI techniques, simple and improved delay-dependent robust stability criteria, which are given in terms of quadratic forms of state and LMI, are derived. The proposed results are applicable to robust control design.
"Other asymptotic stability criteria have been proposed in Su and Chu (1999) and Su et al. (2002), this result was obtained via the Lyapunov function and linear matrix inequalities (LMI) techniques approach independent of the size of the delays (Boyd et al. 1994). Using Lyapunov– Krasovskii functionals combined with LMI techniques for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws (Liu 1995, 2005, Cao et al. 2002, Su et al. 2002). However, in the control of time-delay saturating actuator systems, it is usually desirable to design a controller that not only robustly stabilizes the system, but also estimates the bound of delay time h to keep the stabilization of the system. "
[Show abstract][Hide abstract] ABSTRACT: This paper discusses the problems of the delay-dependent robust stability and stabilization for a class of linear time-delay uncertain systems with saturating actuators. Some new delay-dependent stability criteria are derived by taking the relationships between the terms in the Leibniz–Newton formula into account. The stability conditions are formulated as linear matrix inequalities that can be easily solved by various convex optimization algorithms or computing software. Moreover, the stability criteria are extended to the design of a stabilizing state feedback controller. Numerical examples demonstrate that these criteria are effective and are an improvement on previous ones.
International Journal of General Systems 02/2011; 40(3):301-312. DOI:10.1080/03081079.2010.542414 · 1.64 Impact Factor
"The main objective of this article is to design linear dynamic output feedback controllers, which ensure global uniform asymptotic stabilisation for any time delay not larger than a given bound. The most striking feature of these results eliminates the need to involve any turning of parameters, as in the case with robust stabilisation (Su et al. 2002; Liu, 2005), and it can be computed effectively (Liu 1995). Two illustrate examples are worked out to show the usefulness of the theoretical results. "
[Show abstract][Hide abstract] ABSTRACT: In this article, the problem of delay-dependent robust stabilisation via dynamic output feedback controllers for time-delay saturating actuator systems with norm-bounded parameter uncertainty is addressed. Instead of applying the Lyapunov function, properties of the comparison theorem and the matrix measure with the model transformation technique are employed to investigate the problems. The sufficient condition for robust stabilisation of input-delay systems with saturating actuators subjected to parametric perturbation is also derived. Both results give an estimate of the maximum time delay, which preserves robust stabilisation. Moreover, an algorithm is proposed to synthesise a dynamic feedback controller for guaranteeing the asymptotic stabilisation of the uncertain time-delay saturating systems. Numerical examples are given to indicate significant improvements over some existing results.
International Journal of Systems Science 11/2010; 41:1273-1280. DOI:10.1080/00207720802011332 · 2.10 Impact Factor
"Stabilization analysis and synthesis of uncertain time delay systems with saturating actuators is an important issue addressed by many authors and for which surveys can be found in several monographs (Han and Mehdi, 1998; Su et al., 1991; 2001; 2002). Recently, one of the important issues is to maximize the allowable delay size for robust stabilization of uncertain time delay systems (Liu et al., 2001; Su et al., 2001; 2002). "
[Show abstract][Hide abstract] ABSTRACT: This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
International Journal of Applied Mathematics and Computer Science 01/2005; 15:45-51. · 1.23 Impact Factor
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