An investigation of the input-to-state practical stability (ISpS) and integral (iISpS) nonlinear systems with time delays (NSWTDs) is presented in this paper. The ISpS iISpS are obtained by using a continuously differentiable Lyapunov–Krasovskii functional (LKF) within-definite derivative, which generalizes classical LKF positive definite derivative. As result, uniform asymptotic (UPAS) criteri...

This article presents a novel approach to assess the stability of linear systems with delayed and sampled-data inputs. It proposes an extension of existing results on the stability of sampled-data systems to the case where a delay is introduced in the control loop. The method is based on a continuoustime modelling of the systems together with the discrete-time Lyapunov theorem, which provides e...

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using max-separable ISS Lyapunov function method, a sufficient condition is given general NIPS. On that basis, criteria linear (LIPS) affine (ANIPS) are given. Through them, properties can be directly judged from algebraic differential characteristics systems. ...

Correctness of many hybrid and distributed systems require stability and convergence guarantees. Unlike the standard induction principle for verifying invariance, a theory for verifying stability or convergence of automata is currently not available. In this paper, we formalize one such theory proposed by Tsitsiklis [25]. We build on the existing PVS metatheory for untimed, timed, and hybrid in...