The computation of the viability kernel for switched systems

Abstract

Abstract The computation of the viability kernel provides the guarantee for the security evolution of the systems. In this paper, we focus on the computation of the viability kernel for discrete-time and continuous-time switched systems. A connection between the backward reachable set and the viability kernel for switched systems is established. The methods of computing the viability kernel for switched systems are constructed by using this connection. First, a method of computing the viability kernel for discrete-time switched systems is proposed. Then, taking into account the special structure of switched linear systems, a simple algorithm that is easy to implement is developed. Moreover, the methods of dealing with the discrete systems are extended to the continuous systems, and the algorithms of computing the viability kernel for continuous-time switched systems and switched linear systems are proposed. Finally, examples are listed to illustrate the effectiveness of the main results.

Keywords

• Switched systems
• Control
• Viability kernel
• Reachable set