Input-to-State Stability of Nonlinear Impulsive Systems

Lyapunov conditions for input-to-state stability of impulsive systems

This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equationsmost of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics a...

Input-To-State Stability of Nonlinear Functional Systems

Constrained Input-to-state Stability of Nonlinear Systems

Input-to-state stability (ISS), integral-ISS (iISS) and their related notions of input/output stability and detectability have become a useful framework for nonlinear feedback analysis and design. In this paper, a new notion, that of constrained input-to-state stability (cISS), is presented and several characterizations of cISS are obtained. cISS, unlike ISS or iISS, is not confined to forward ...

Input-to-state Stability of Switched Nonlinear Systems

The input-to-state stability (ISS) problem is studied for switched systems with infinite subsystems. By the method of multiple Lyapunov function, a sufficient ISS condition is given based on a quantitative relation of the input and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some suffic...

Input-to-state stability for discrete-time nonlinear systems

In this paper the input-to-state stability (iss) property is studied for discrete-time nonlinear systems. We show that many iss results for continuoustime nonlinear systems in earlier papers (Sontag, 1989; Sontag, 1990; Sontag and Wang, 1996; Jiang et al., 1994; Coron et al., 1995) can be extended to the discretetime case. More precisely, we provide a Lyapunov-like sufficient condition for iss,...