2017/09/19 by Liying Zhu, Jianbin Qiu · 12 citations
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Computer science #Control (management) #Control theory (sociology) #Controller (irrigation) #Counterexample #Differential equation #Discrete mathematics #Equilibrium point #Exponential stability #Instability #Limit (mathematics) #Linear system #Lyapunov function #Mathematical analysis #Mathematics #Nonlinear system #Stability (learning theory) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Stability theory
paper · doi:10.1080/00207179.2017.1381883
published in International Journal of Control 92(5), 1061-1083 (Taylor & Francis)
openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
This paper studies stability and stabilisation issues of switched linear time-invariant systems with stable/unstable multiple equilibria. Investigation of such switched systems is motivated by a switching economic system. The well-known common Lyapunov function method is shown to be ineffecctive in analysing region stability of switched systems with multiple equilibria via a counterexample. When every subsystem has an equilibrium point and all multiple equilibria pairwise differ, this paper proposes some sufficient conditons for region stability/instability of such switched systems with respect to a region containing all multiple equilibria under arbitrary quasi-periodical switchings. These novel results imply that there may exist stable limit cycles of such switched systems. Based on the stability results, a global asymptotic region-stabilising controller, quasi-periodical switching path, and corresponding algorithm are all designed for such switched control systems. Several illustrative examples demonstrate the effectiveness and practicality of our new results.