Abstract
In this paper, the stability analysis and controller design of two-dimensional (2-D) switched system with random disturbances are studied. First, based on the Fornasini–Marchesini local state space model, a random discrete 2-D switched system model is proposed. Secondly, based on the method of switching quadratic Lyapunov function, Schur complement and linear matrix inequality the criterion of the sufficiency of the asymptotically stable under any switching signal is established. The extended average residence time method is used to obtain a sufficient criterion of the mean square exponential stability of the random discrete 2-D switched system under restricted switching conditions. According to the stability analysis results, the conditions for the existence of the state feedback controller are given and the corresponding state feedback controller is designed. Finally, two examples are given to illustrate the effectiveness of the proposed method.
Highlights
In recent decades, many researchers have received significant attention from the related theoretical research of 2-D systems
System stability under restricted switching laws: The switched system may not be stable under arbitrary switching, but the system may be stable under restricted switching signals, such as a closed-loop multi-controller system
The discrete-time 2-D switched system (8) is asymptotically stable if there exist matrices P(l) > 0, P(k) > 0 and Q(k) > 0, ∀k, l ∈ Nsuch that the following linear matrix inequality(LMI) holds:
Summary
Many researchers have received significant attention from the related theoretical research of 2-D systems. Discrete-time 2-D systems have gradually become an important research direction of 2-D systems with the rapid development of science and technology. It can be seen in [2–4], the stability analysis problem of the 2-D system has been solved. Even if all subsystems are unstable, the stability of the discrete-time switched system can be guaranteed by appropriate switching signals. In [14], the stabilization problem of 2-D switched systems represented by the FM local state space model and the Roesser model is addressed by switching signal conditioning. Badie et al [18] studied the problem of time-delay-dependent exponential stability analysis of 2-D discrete switched systems with time-varying delays described by the Roesser model. Even if every subsystem in the system is in a stable state, the entire 2-D switched system may be unstable under a specific switching signal
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