Time scale state feedback h-stabilisation of linear systems under Lipschitz-type disturbances

Abstract

This paper studies the h-stabilisation problem of certain classes of perturbed systems on time scales. Sufficient conditions for the control law design are proposed to ensure the h-stability of the closed-loop dynamical system under Lipschitz-type disturbances. Using the Gronwall inequality approach with time scale theory, the h-stability of the closed-loop system is investigated in non-uniform time domains with bounded graininess. Some numerical examples are provided to show the feasibility of the obtained results using the proposed approach for systems evolving on some arbitrary time scales.