Novel Approaches to Stability and Stabilization of Positive Switched Systems with Unstable Subsystems
This paper investigates the globally uniformly exponential stability of positive switched linear system (PSLS) in both continuous-time and discrete-time contexts. By using the multiple piecewise-continuous linear copositive Lyapunov function (MPLCLF) and exploring mode-dependent average dwell time (MDADT) switching, several stability criteria are developed with a switching strategy where slow switching and fast switching are applied to stable and unstable subsystems respectively. The proposed methods are also used to stabilize PSLS with controllable and uncontrolled subsystems. The obtained results provide lower bounds on MDADT of stable subsystems and higher bounds on MDADT of unstable subsystems and reduce the conservatism compared with the existing results. Finally, two numerical examples are provided to validate the advantages of the obtained results.
KeywordsPositive systems Mode-dependent average dwell time Multiple copositive Lyapunov function Switched systems Linear programming
This work was supported by the National Science Foundation of China under Grants 61773089, 61374070, 61473055, the Fundamental Research Funds for the Central Universities under Grants DUT17JC14, DUT17ZD227, and Youth Star of Dalian Science and Technology under 2016RQ014, 2015R052.
- 1.Farina L., Rinaldi S.: Positive Linear Systems: Theory and Applications. Wiley, New Jercy (2011)Google Scholar
- 2.Jadbabaie A., Lin J., Morse A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. In: Proceedings 41st IEEE Conference on Decision and Control (2002)Google Scholar
- 5.Fei, Z., Shi, S., Wang, Z., Wu, L.: Quasi-time-dependent controller and filter design for discrete-time switched system with mode-dependent average dwell time. IEEE Trans. Autom. Control PP(99), 1–1 (2017)Google Scholar
- 8.Rami M., Tadeo F.: Positive observation problem for linear discrete positive systems. In: Proceedings 45th IEEE Conference on Decision and Control, pp. 4729–4733 (2006)Google Scholar