Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

Jose Luis Mancilla-Aguilar, Hernan Haimovich

2020IEEE Transactions on Automatic Control43 citationsDOI Open Access PDF

Abstract

We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and time-varying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.

Topics & Concepts

Control theory (sociology)Scalar (mathematics)Stability (learning theory)Lyapunov functionMathematicsReduction (mathematics)Exponential stabilityStability conditionsControl systemLinear systemStability criterionLyapunov equationFunction (biology)Applied mathematicsComputer scienceLyapunov stabilityStability theoryNumerical stabilityMultidimensional systemsStability and Control of Uncertain SystemsNeural Networks Stability and SynchronizationNonlinear Differential Equations Analysis