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Article

New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems

1
Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy, Hubei University of Technology, Wuhan 430068, China
2
Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan
3
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
*
Author to whom correspondence should be addressed.
Academic Editor: Olivier Sename
Electronics 2022, 11(13), 1963; https://doi.org/10.3390/electronics11131963
Received: 1 June 2022 / Revised: 17 June 2022 / Accepted: 20 June 2022 / Published: 23 June 2022
Global quadratic stability and L2 performance in probability (quadratic stability and L2 gain γ in probability: abbreviated as GQL2(γ)-P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQL2(γ)-P, it is shown that if there exists a convex combination of subsystems achieving GQL2(γ)-P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQL2(γ)-P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm. View Full-Text
Keywords: switched uncertain stochastic systems (SUSS); state-dependent switching laws; norm-bounded uncertainties; global quadratic ℒ2 performance γ in probability (GQℒ2(γ)-P); convex combination; linear matrix inequalities (LMIs) switched uncertain stochastic systems (SUSS); state-dependent switching laws; norm-bounded uncertainties; global quadratic ℒ2 performance γ in probability (GQℒ2(γ)-P); convex combination; linear matrix inequalities (LMIs)
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MDPI and ACS Style

Chang, Y.; Zhai, G.; Xiong, L.; Fu, B. New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems. Electronics 2022, 11, 1963. https://doi.org/10.3390/electronics11131963

AMA Style

Chang Y, Zhai G, Xiong L, Fu B. New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems. Electronics. 2022; 11(13):1963. https://doi.org/10.3390/electronics11131963

Chicago/Turabian Style

Chang, Yufang, Guisheng Zhai, Lianglin Xiong, and Bo Fu. 2022. "New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems" Electronics 11, no. 13: 1963. https://doi.org/10.3390/electronics11131963

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