Improved robust H∞ exponential mean square stabilization for uncertain Markov jump delay systems based on memory‐state feedback control

Abstract

Abstract This paper investigates the problem of robust H∞ exponential mean square stabilisation for uncertain Markov jump systems with time‐varying and mode‐dependent delays based on memory‐state feedback control. Attention is focused on the design of memory‐state feedback controller for uncertain Markov jump systems with time‐varying and mode‐dependent delays such that the closed‐loop uncertain Markov jump systems satisfies robust H∞ exponential mean square stability. The improved conditions for the solvability of the memory‐state feedback control problem are obtained via designing mode‐dependent and delay‐dependent L‐K functional. The desired memory‐state feedback controller is given by using linear matrix inequalities. Two simulation examples including a numerical example and a practical example of the industrial non‐isothermal continuous stirred tank reactor are used to demonstrate the effectiveness and usefulness of the delayed feedback control technique that this paper proposes.

Keywords

• Interpolation and function approximation (numerical analysis)
• Algebra
• Markov processes
• Linear control systems
• Control system analysis and synthesis methods
• Stability in control theory