Stability of Switching Time Delay Systems
1. School of Electric Engineering and Automation, Dalian Jiaotong University, Dalian 116028, China
2. School of Mathematics, Dalian Jiaotong University, Dalian 116028, China
3. School of Software, Dalian Jiaotong University, Dalian 116028, China
| Abstract: | Switched systems, as a kind of system models with multi-modal characteristics, Therefore, switched systems have important theoretical research value. In this paper, Lyapunov function and model dependent average dwell time method (MDADT) is used to study the exponential stability of nonlinear and linear switched time delay systems. The mode dependent average dwell time scheme is introduced into the system with switched time delay. Based on the mode dependent average dwell time design, the sufficient conditions for exponential stability are given in the form of linear matrix inequalities (LMIs). Exponential stability for switched delay systems consisting of stable and unstable subsystems is addressed. Under the condition that activation time ratio between stable subsystems and unstable ones is not less than a specified constant, sufficient conditions are given to guarantee exponential stability of the switched delay systems. Subsequently, for a special class of switched delay systems, a lower bound on the mode dependent average dwell time and the activation time ratio of subsystems are calculated respectively by solving a set of linear matrix inequalities (LMIs) and certain equations. The concrete form of state exponential decay of the system is given. It is proved that under the condition of arbitrary switching, all the signals in the switched closed loop system are finally bounded, each subsystem output can track the corresponding target trajectory within a small bounded error range. Finally, the effectiveness of the proposed method is demonstrated by numerical examples and MATLAB simulation. |
| Keywords: | Mode Dependent Mean Dwell Time; Switched Delay Systems; Exponential Stability; Lyapunov Function; Linear Matrix Inequality (LMI) |
| DOI: | 10.57237/j.se.2023.04.001 |
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Received: 5 May 2023
Accepted: 25 June 2023
Published Online: 29 August 2023
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