Robust interval stability/stabilization and H∞ feedback control for uncertain stochastic Markovian jump systems based on the linear operator

This paper focuses on the problem of robust H∞ state feedback control with interval pole constraints for uncertain stochastic Markovian jump systems (MJSs). First, we present the sufficient conditions of robust interval stability using a linear operator and its spectrum. A robust interval stabilization controller is designed for MJSs; it ensures the stability of MJSs and adjusts the rate of convergence. In addition, the robust H∞ controller with interval pole constraints is designed with the admissible parametric uncertainties and a prescribed H∞ disturbance attenuation level; this guarantees that the closed-loop system is robust and asymptotically stable with an ideal rate of convergence. A numerical example is provided to demonstrate the effectiveness of the proposed method.