Local Stabilization for a Class of Nonlinear Impulsive Switched Systems with Norm-Bounded Input: A Matrix Inequality Approach

This paper investigates stabilization for a class of nonlinear impulsive switched systems with norm-bounded input constraint. Due to this constraint, it is only enough that the stabilization criteria and assumptions related to the nonlinearities be met on a subspace containing the origin. Certainly, these assumptions are such that they covers most of real-world systems. The purpose of this paper is to design a norm-bounded control that guarantees the exponential convergence of trajectories to a sufficient small ultimate bound in presence of uncertainties. Therefore, firstly, we present the stability criteria for a general model that ensures the convergence of all trajectories starting from a region of attraction to an ultimate bound. These conditions are in terms of a common Lyapunov function candidate and the minimum dwell-time, and it is enough to be valid on the region of attraction. Secondly, using the common quadratic Lyapunov function candidate and using the state-feedback approach, the established conditions are reformulated as a set of linear or bilinear matrix inequalities. Besides, to achieve the control parameters along with the largest convergence area and smallest ultimate bound, we propose an optimization problem. Finally, some illustrative examples are presented to demonstrate the proposed approach.