Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy
Abstract
:1. Introduction
- Differently from the existing works, the commonly adopted convex stable combination assumption is relaxed in this paper. It is shown that the relaxed assumption guarantees the stability of the switched systems with a small time delay under the min-projection switching strategy. Hence, the method we are to develop can be applied to a larger class of switched systems;
- In contrast to existing works, some of the main sources of conservatism in the stability analysis are overcome by introducing slack variables into the relaxed assumption and using a reciprocally convex inequality (Lemma 6) to handle the terms associated with the delay arising in the Lyapunov analysis. Therefore, our method leads to a less conservative delay bound, as will be shown by the numerical examples in Section 4;
- The stability issues associated with possible sliding motion are carefully addressed in this paper, whereas these issues are usually circumvented in the existing literature. Moreover, by utilizing the memory of switching signals, a modified min-projection switching strategy is proposed to avoid the occurrence of sliding motion;
2. Problem Statement and Preliminaries
2.1. Problem Statement
2.2. The Min-Projection Switching Strategy and Its Properties
2.3. Some Technical Lemmas
3. Results
- (1)
- Specify the initial mode i according to min-projection switching strategy (7), i.e., ;
- (2)
- Stay in the mode as long as
- (3)
- Otherwise, switch to the next mode according to the min-projection switching strategy (7) and go back to Step 2.
4. Numerical Examples
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Hou, T.; Li, Y.; Lin, Z. Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy. Actuators 2021, 10, 261. https://doi.org/10.3390/act10100261
Hou T, Li Y, Lin Z. Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy. Actuators. 2021; 10(10):261. https://doi.org/10.3390/act10100261
Chicago/Turabian StyleHou, Tan, Yuanlong Li, and Zongli Lin. 2021. "Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy" Actuators 10, no. 10: 261. https://doi.org/10.3390/act10100261