Converse theorem for practical stability of nonlinear impulsive systems and applications

Abstract

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Exponential Stability of Impulsive Cascaded Systems and its Application in Robot Control

“…where θ 1 , θ 1 : R + −→ R + are two continuous functions [27], [28], [33], [38]- [40], [47], [48]. Contrary to what we mentioned above, in Theorem 5 the boundedness of the solutions is not a necessary condition to guarantee the convergence of the cascaded system; moreover, the condition imposed on the interconnection term g(t, x) between the two subsystems is more general than condition (20), and than the one mentioned in [37].…”

“…Recently, using a converse theorem for the practical exponential stability of impulsive systems, [47] established the practical exponential stability of cascaded impulsive systems. More recently, and in a similar spirit, the practical asymptotic stability of cascaded impulsive systems was elaborated in [48].…”

converse theorem for practical $h$-stability of time-varying nonlinear systems

“…The stability of dynamical systems is the most important criterion in systems design (see [6, 14,16,20]). The primary objective of a Lyapunov function is to analyze the behavior of trajectories of a dynamical system and how this behavior is preserved after perturbations (see [10,15]). It gives sucient conditions for stability, asymptotic stability, and so on.…”