Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi-Sugeno (T-S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T-S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T-S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H∞ and passivity performance. Based on this new performance index, the weighted H∞ control problem and the passive control problem for switched T-S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T-S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.