A direct Lyapunov condition for strong uniform stability of impulsive systems

HERNAN HAIMOVICH; JOSÉ L. MANCILLA-AGUILAR

Congreso; 27º Congreso Argentino de Control Automático AADECA?20 Virtual; 2020

AADECA

The most usual asymptotic stability properties forimpulsive systems ensure decay towards equilibrium as timeelapses, irrespective of the number of impulses that occur. Veryrecent results have shown that not considering the number ofoccurring impulses in the stability property results in the lack ofspecific types of robustness. By ?strong stability? we refer to thesuitably modified property that takes impulse occurrence intoaccount and has been shown to regain the required robustness.Existing results based on Lyapunov-type functions, which mayprovide sufficient conditions for strong stability, can be appliedto a limited class of systems and constitute stringent conditions,far from being necessary. In this work, we provide a novel directLyapunov result to establish strong global uniform asymptoticstability for (time-varying, nonlinear) impulsive systems. Weprovide examples to illustrate that none of the assumptionsrequired in the Lyapunov condition can be removed, thus showingthat such assumptions are not contrived.