Comments on integral variants of ISS
Systems & Control Letters
Input-to-state stability for discrete-time nonlinear systems
Automatica (Journal of IFAC)
Input-to-State Stabilization with Quantized Output Feedback
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Brief paper: Delay-dependent stability of reset systems
Automatica (Journal of IFAC)
ACC'09 Proceedings of the 2009 conference on American Control Conference
Admissible control for a class of switched and descriptor systems with impulsive effects
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Brief paper: Exponential stability of nonlinear time-delay systems with delayed impulse effects
Automatica (Journal of IFAC)
Input-to-state stability of impulsive and switching hybrid systems with time-delay
Automatica (Journal of IFAC)
Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics
Automatica (Journal of IFAC)
On controller initialization in multivariable switching systems
Automatica (Journal of IFAC)
Input-to-state stability of interconnected hybrid systems
Automatica (Journal of IFAC)
Finite data-rate feedback stabilization of switched and hybrid linear systems
Automatica (Journal of IFAC)
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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 equations most 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 are ISS, but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS, but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS, and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case, we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network.