Abstract
In this chapter, the stability problem is investigated for some classes of differential systems under the influence of switching and impulsive actions. The Lyapunov direct method is used. It is assumed that Lyapunov function constructed for the considered system satisfies the non-stationary differential inequality with hybrid degrees. Especially interesting for analysis is the case where non-stationary coefficients in this differential inequality disappear with time, or, on the contrary, increase unboundedly. Some examples of dynamical systems, for which one can apply the obtained results, are considered. So, hybrid complex systems with linear and nonlinear subsystems are studied. Also, a class of nonlinear mechanical systems with non-stationary switched force fields is investigated.KeywordsImpulsive switched systemsStabilityLyapunov functionsNon-stationary differential inequalities
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