Stability analysis of Markovian jump systems with delayed impulses

Abstract

This paper addresses stability for Markovian jump systems with delayed impulses. The delayed impulse has a largely negative effect on the system stability and is not easy to be studied. The main reason is that so many factors such as Markovian switching, impulse, and time‐varying delay are simultaneously contained and make its analysis complicated and difficult. In order to analyze these factors clearly, some novel enlarging techniques are presented and used to establish linear matrix inequality (LMI) conditions ultimately. Based on the given methods, more situations such as impulsive instant sequence satisfying a renewal process and Poisson process, respectively, are further studied and better than ones without considering such properties. Two numerical examples are used to show the effectiveness and superiority of the methods.

Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

“…The positive definite matrices Q i and R i related to the cost function ( 2) are all chosen as identity matrices with appropriate dimensions. First, algorithm ( 15) is used to approach the unique positive definite solution of SCARE (5). With zero initial values, the associated convergence curves can be plotted.…”

“…Many practical systems suffer from sudden changes in structure and parameters caused by component failures or maintenance, or sudden environmental interference is quite common, such as electrical power systems [1], robot manipulator systems [2,3], and communication systems [4,5]. The models with Markovian jumps are often used to describe such systems; therefore, the problems for systems with Markovian jumps are widely considered and studied, including optimal control [6,7], filter design [8], stabilization [9][10][11], observability and detectability problem [12], and so on.…”

Exponential stability of time‐delay systems with flexible delayed impulse

“…Such impulses related to historical states are more applicable to the real system. Much work on control methods and stability analyses for systems with delayed impulses has received attention [32,33]. Khadra et al analyzed the error dynamics of secure communication systems with delays in both impulses and differential systems [9].…”

Necessary and sufficient optimal control conditions for networked control systems with input delay and Markovian packet dropouts

“…Networked control systems (NCSs) are communication control system composed of controller, sensor, actuator, and the control loop through the communication network [1][2][3]. NCSs have advantages of low cost, simple operation, and high reliability, such that they boost application development in UAV, deep-sea exploitation, and some manufacturing systems [4][5][6][7].…”