Robust stability of complex impulsive dynamical systems

Abstract

This paper investigates stability for systems with practical levels of complexity including nonlinearities, large-scale interconnections, time-delays, uncertainty and heterogenous signals, in this case chosen to be impulses in continuous-time. More precisely, the results give robust global exponential stability (RGES) for complex impulsive dynamical systems. By utilizing Lyapunov function and Lyapunov-Krasovskii functional methods, two types of criteria are derived under each of which RGES is achieved. These criteria are expressed in terms of LMIs and algebraic inequalities. Meanwhile, the estimation of the decay rate is also obtained. Furthermore, the results are used to design an impulsive controller under which RGES is achieved for a closed-loop large-scale interval continuous systems with multi-coupling time-delays. The impulsive controller can be easily obtained by solving the derived LMIs and algebraic inequalities. One example with numerical simulations is worked out for illustration.