Stabilization of impulsive quadratic systems over polytopic sets

This paper deals with the stabilization of Impulsive Dynamical Systems (IDSs) which represent a subclass of hybrid systems. The IDSs considered here are described by a continuous-time dynamics defined by a nonlinear quadratic system and exhibit discrete jumps in the state trajectory. In this paper we provide sufficient conditions for the design of both static state- and dynamical output-feedback controllers. The proposed conditions guarantee, for the closed-loop system, the local asymptotic stability of the zero equilibrium point, and the inclusion of a given polytopic region into the domain of attraction of the equilibrium itself. Specialized conditions are provided for the case of time-dependent quadratic IDSs with prescribed resetting times. The proposed results require the solution of a feasibility problem involving Linear Matrix Inequalities (LMIs), which can be efficiently solved by using off-the-shelf optimization algorithm, as shown through numerical examples.