A new approach based on state conversion to stability analysis and control design of switched nonlinear cascade systems

Abstract

In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF can be constructed by employing the back-stepping approach. The major shortcoming of the SDL is that this limitation cannot be satisfied for complicated switched nonlinear systems. Therefore, a CQLF cannot be constructed by employing the back-stepping approach. Moreover, if SDL is satisfied, only stabilization problem can be solved. In this paper, a new approach based on state transformation is introduced to solve the stabilization and control problems of switched nonlinear cascade systems without any limitation. Several simulation and experimental studies are provided to show the effectiveness of the proposed approach.