H∞ control for Markov jump systems with multi-timescale characteristic based on slow state feedback

This paper investigates the control problem of Markov jump systems with multi-time scales.Leveraging singular perturbation theory, a design method for a control protocol based on slow state feedback is presented.Moreover, by employing the Lyapunov stability theory and selecting a Lyapunov function associated with small singular perturbation parameter, several adequate requisites for the stability of the system are derived.The estimation method for the upper bound of singular perturbation parameters is also provided.Finally, a numerical simulation is conducted using Matlab software.The simulation results for the system with and without performance indicators are presented respectively, thus verifying the validity of the acquired conditions.