Input-to-state stability of impulsive and switching hybrid systems with time-delay

• DOI: 10.1016/j.automatica.2011.01.061
• Publication Date: 2011-02-27T08:44:52Z
• Authors: Jun Liu; Xinzhi Liu; Wei-Chau Xie
• Keywords: 0209 industrial biotechnology; 02 engineering and technology

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov-Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense, provided that there are no overly long intervals between impulses, i.e., the impulsive and switching signal satisfies a dwell-time upper bound condition. Moreover, these impulsive ISS/iISS stabilization results can be applied to systems with arbitrarily large time-delays. Conversely, in the case when all the subsystems governing the continuous dynamics are ISS/iISS in the absence of impulses, the ISS/iISS properties can be retained if the impulses and switching do not occur too frequently, i.e., the impulsive and switching signal satisfies a dwell-time lower bound condition. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.