Robust Control of A Class of Uncertain Switched Nonlinear Systems in the Presence of Disturbances: A Passivity Approach

In this paper, the problem of robust stabilization of uncertain and perturbed switched nonlinear systems has been investigated. It’s well-known that the solution of H∞ control problem may not exist for switched systems with a common storage function for all subsystems. On the other hand, by adopting multiple storage functions, different Hamilton-Jacobin inequalities need to be solved. Hence, the robust control problem is addressed here based on passivity, in two cases. First, it is assumed that there is at least one passive subsystem in the whole state space, and the problem is solved based on the average dwell time approach. In this case, by defining the concept of system passivity rate, the admissible range of average dwell time is obtained. In the second case, none of subsystems is passive and the H∞ control problem is solved by using the feedback passification. In addition to theoretical analysis of the design algorithms, the performance of the theorems for uncertain switched nonlinear systems has been investigated by providing two simulation examples and numerical analysis.