Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems With Time Delay
Bao Wang, Quanxin Zhu, Subei Li
Abstract
The stability and stabilization problems for discrete-time semi-Markov jump linear systems with time delay are discussed. By virtue of a novel Lyapunov–Krasovskill functional and the probability structure of semi-Markov switching signal, the sufficient stability conditions for the considered systems are presented in terms of a set of linear matrix inequalities and a proper semi-Markov switching condition. Based on such conditions, the time delay and mode dependent controller can be designed to stabilize the corresponding closed-loop systems. Finally, two examples are given to illustrate the effectiveness of our results.
Topics & Concepts
Control theory (sociology)Markov chainDiscrete time and continuous timeMathematicsLinear systemStability (learning theory)Markov processController (irrigation)Computer scienceControl (management)Mathematical analysisStatisticsBiologyAgronomyArtificial intelligenceMachine learningStability and Control of Uncertain SystemsNeural Networks Stability and SynchronizationStability and Controllability of Differential Equations