Stabilization of impulsive quadratic systems over polytopic sets

作者：Amato F; Ambrosino R; Cosentino C^*; De Tommasi G; Merola A

来源：Nonlinear Analysis: Hybrid Systems , 2013, 7(1): 16-27.

DOI：10.1016/j.nahs.2012.07.005

• Impulsive dynamical systems
• Quadratic systems
• Domain of attraction
• Stabilization

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.

• 出版日期2013-2