Design of simultaneous static output feedback low‐gain H_∞ controllers for a collection of time‐delay system

Abstract

Summary This paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.

On the simultaneous stabilization of stochastic nonlinear systems

“…Remark 3. Inequality (26) shows that in the setting of simultaneous stochastic systems, a continuous feedback p simultaneously stabilizes the collection of systems in (1) has to verify for each i ∈ I,…”

Convergence of the optimization method for feedback stabilization of linear delay systems

“…For the stabilization of time-delay systems, based on the Riccati equation, a feedback low-gain controller is proposed by solving a minimization problem. 15 In Reference 16, by an augmented Lyapunov functional and linear matrix inequalities (LMIs)-based conditions, a family of local state-feedback schemes are designed to guarantee that the closed-loop subsystem enjoys the delay-dependent asymptotic stability. Recently, in Reference 17, Hu proposes a new necessary and sufficient condition for feedback stabilization of linear time-delay control systems based on the state transition matrix of the closed-loop system for the first time.…”

“…In Reference 14, according to Lyapunov theory, the designs of state feedback controllers for iterative algorithms based on linear matrix inequalities (LMIs) have been extensively studied. For the stabilization of time‐delay systems, based on the Riccati equation, a feedback low‐gain controller is proposed by solving a minimization problem 15 . In Reference 16, by an augmented Lyapunov functional and linear matrix inequalities (LMIs)‐based conditions, a family of local state‐feedback schemes are designed to guarantee that the closed‐loop subsystem enjoys the delay‐dependent asymptotic stability.…”

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

“…Thus, it is necessary to consider time delays and modeling uncertainties for the problem of simultaneous stabilization. However, a few papers have been devoted to the study of simultaneous stabilization of time-delay systems (Mahmoud and Nounou, 2006; Korovin et al., 2011; Minyaev and Fursov, 2012, 2013; Cai, 2015; Jialing and Jundong, 2015; Wu et al., 2017).…”

“…(2018), the problem of constructing a simultaneously stabilizing controller for a set of single-input feedback linearizable time-delay systems with uncertain parameter was considered. Wu et al. (2017) developed a method to solve the simultaneous static output feedback low-gain H∞-control problem for a collection of linear systems with both state and input delays on the basis of an optimization technique.…”