Stabilizing control of Markovian jump systems with sampled switching and state signals and applications

Abstract

This article addresses the stabilization problem of continuous‐time Markovian jump systems (MJSs). Because of both switching and state signals sampled, a novel system with an exponential matrix characterizing the sampling effects is developed. It is used to be an auxiliary system and plays important roles in system analysis and synthesis. Sufficient stabilization conditions are presented and fully consider the sampling rate. The applications of established methods and results are applied to networked control in the presence of denial‐of‐service (DoS). The frequency and duration of DoS attacks ensuring stability of the closed‐loop system are characterized. Meanwhile, more special situations about particular transition rate matrix, sampling logic and improved mode‐dependent controller are considered respectively. The analysis results are significant and bring an important method to study the control for MJSs with sampled switching and state signals. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.

Event‐triggered output feedback H∞$$ H\infty $$ control for Markovian jump networked control systems with signal quantization

“…It has been widely used in industrial control systems, networked control systems, fault detection systems and other fields. [1][2][3][4][5][6][7][8][9] It has attracted many scholars to study the stability analysis and controller design of Markovian jump systems. Zhang and Lu based on Kronecker product and 𝜇 analysis by means of transforming the problem into a method to test whether a class of uncertain matrices is nonsingular and to judge the nonsingularity of uncertain matrices, the disturbance bound of robust stochastic stability of the studied system and the exact upper and lower bounds of robust H 2 performance are obtained.…”

“…Over the past decades, there has been significant interest in the field of Markovian jump systems, as a special class of stochastic hybrid systems, have the advantage of well describing physical systems with abrupt changes. It has been widely used in industrial control systems, networked control systems, fault detection systems and other fields 1–9 . It has attracted many scholars to study the stability analysis and controller design of Markovian jump systems.…”