Stabilization and robust H∞H∞ control for sector-bounded switched nonlinear systems

This paper presents stability analysis and robust H∞H∞ control for a particular class of switched systems characterized by nonlinear functions that belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system but without making additional assumptions (e.g. on the derivative of the nonlinear functions), and by proposing new multiple Lyapunov function candidates, we formulate stability conditions and a control design procedure in the form of matrix inequalities. The proposed Lyapunov functions are more general than the quadratic functions previously proposed in the literature, as they incorporate the nonlinearities of the system and hence, lead to less conservative stability conditions. The stabilizing switching controllers are designed through a bi-level optimization problem that can be efficiently solved using a combination of a convex optimization algorithm and a line search method. The proposed optimization problem is achieved using a special loop transformation to normalize the arbitrary sector bounds and by other linear matrix inequalities (LMI) techniques.