Robust exponential quasi-passivity and global stabilization for uncertain switched nonlinear systems

In this article, a concept of robust exponential quasi-passivity for uncertain switched nonlinear systems is first proposed to describe the overall exponential quasi-passivity property in the absence of the exponential quasi-passivity property of the subsystems. Compared to passive systems, quasi-passive system that may contain sources of energy can produce energy itself. On this basis, several issues including robust exponential quasi-passivity conditions, feedback robust exponential quasi-passification, and globally practical stabilization for switched nonlinear systems with structural uncertainties are investigated. First, a more general switching law is designed to render uncertain switched nonlinear systems robust exponentially quasi-passive. This result is generalization of robust KYP Lemma. Second, the feedback robust exponential quasi-passification problem for uncertain switched nonlinear systems is solved by the co-design of a state-dependent switching law and state feedback controllers. Third, an robust exponentially quasi-passive switched nonlinear system under a given switching signal is shown to be practically stabilized by a set of output feedback controllers. Furthermore, the obtained results are applicated to solve globally practical stabilization problem for uncertain switched nonlinear systems whose subsystems have any same relative degree by combining the proposed robust exponential quasi-passification method with backstepping technique. Moreover, a set of feedback controllers and a state-dependent switching law are designed constructively. Finally, the proposed methods are applied to the investigation of a switched continuous stirred tank reactor system.