Nonfragile stabilization for semi-Markovian switching systems with actuator saturation via improved dynamic event-triggered scheme
Miaohong Luo
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorXihui Wu
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorCorresponding Author
Xiaowu Mu
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Correspondence Xiaowu Mu, School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China.
Email: [email protected]
Search for more papers by this authorZhe Yang
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorMiaohong Luo
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorXihui Wu
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorCorresponding Author
Xiaowu Mu
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Correspondence Xiaowu Mu, School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China.
Email: [email protected]
Search for more papers by this authorZhe Yang
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
Search for more papers by this authorFunding information: Foundation of Henan Educational Committee, 16A110023; National Natural Science Foundation of China, 11971444
Abstract
This article addresses the problem of stabilization and the H∞ performance for semi-Markovian systems with actuator saturation via dynamic event-triggered scheme. Due to actuator degradation and numerical round-off errors, nonfragile control is proposed. Meanwhile, the saturated nonlinearity is considered in the controller design process, which makes the controller design more practical. Furthermore, the improved event-triggered scheme is utilized for reducing transmitting unnecessary sampled data to the network and saving communication cost. By establishing appropriate Lyapunov–Krasovskii functional that depends on model information and using free-weighting matrix techniques, new sufficient conditions for ensuring the stabilization of the controlled systems are obtained. Then the gain matrices of the controller can be also designed. Finally, simulation examples are provided to verify that the results we get are effective.
REFERENCES
- 1Foucher Y, Mathieu E, Saint-Pierre P, Durand JF, Daurès JP. A semi-Markov model based on generalized Weibull distribution with an illustration for HIV disease. Biom J. 2005; 47(6): 825-833.
- 2Li H, Zhao Q. Reliability evaluation of fault tolerant control with a semi-Markov fault detection and isolation model. Proc IMechE Part I. 2006; 220(5): 329-338.
- 3Dai J, Guo G. Event-triggered leader-following consensus for multi-agent systems with semi-Markov switching topologies. Inf Sci. 2018; 459: 290-301.
- 4Kim HK. Stochastic stability and stabilization conditions of semi-Markovian jump systems with mode transition-dependent sojourn-time distributions. Inf Sci. 2017; 385–386: 314-324.
- 5Shi P, Li FB, Wu LG, Lim C-C. Neural network-based passive filtering for delayed neutral-type semi-Markovian jump systems. IEEE Trans Neural Netw Learn Syst. 2017; 28(9): 2101-2114.
- 6 Xu ZW, Wu ZG, Su HY, Shi P, Que HY. Energy-to-peak filtering of semi-Markov jump systems with mismatched modes. IEEE Trans Autom Control. 2020; 65(10): 4356-4361. https://doi.org/10.1109/TAC.2019.2955014.
- 7Zhang H, Wang J, Shi Y. Robust H∞ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities. Syst Control Lett. 2013; 62(12): 1114-1124.
- 8Zhang Y, Xu S, Zhang J. Delay-dependent robust H∞ control for uncertain fuzzy Markovian jump systems. Int J Control Autom Syst. 2009; 7(4): 520-529.
- 9Liu X, Yu X, Zhou X, Xi H. Finite-time H∞ control for linear systems with semi-Markovian switching. Nonlinear Dyn. 2016; 85: 2297-2308.
- 10Huang N, Duan Z, Chen G. Some necessary and sufficient conditions for consensus of second-order multi-agent systems with sampled position data. Automatica. 2016; 63: 148-155.
- 11Liu H, Cheng L, Tan M, Hou ZG. Containment control of continuous-time linear multi-agent systems with aperiodic sampling. Automatica. 2015; 57: 78-84.
- 12Yue D, Han QL, Lam J. Network-based robust H∞ control of systems with uncertainty. Automatica. 2005; 41(6): 999-1007.
- 13Peng C, Ma S, Xie X. Observer-based non-PDC control for networked T-S fuzzy systems with an event-triggered communication. IEEE Trans cybern. 2017; 41(6): 999-1007.
- 14Wu X, Mu X. Event-triggered control for networked nonlinear semi-Markovian jump systems with randomly occurring uncertainties and transmission delay. Inf Sci. 2019; 487: 84-96.
- 15Wu X, Mu X. H∞ stabilization for networked semi-Markovian jump systems with randomly occurring uncertainties via improved dynamic event-triggered scheme. Int J Robust Nonlinear Control. 2019; 29: 4609-4626.
- 16Wang H, Shi P, Lim CC, Xue Q. Event-triggered control for networked Markovian jump systems. Int J Robust Nonlinear Control. 2015; 25: 3422-3438.
- 17Song X, Men Y, Zhou J, Zhao J, Shen H. Event − triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities. Appl Math Comput. 2017; 298: 123-132.
- 18Shen H, Yan H, Karimi HR, Lam HK. Finite-time event-triggered H∞ control for T-S fuzzy Markov jump systems. IEEE Trans Fuzzy Syst. 2018; 26: 3122-3135.
- 19Pradeep C, Cao Y, Murugesu R, Rakkiyappan R. An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach. Math Comput Simul. 2019; 155: 41-56.
- 20 Gong C, Zhu GP, Shi P. Adaptive event-triggered and double-quantized consensus of leader-follower multiagent systems with semi-Markovian jump parameters. IEEE Trans Syst Man Cybern Syst. 2019. https://doi.org/10.1109/TSMC.2019.2957530.
- 21Liu H, Boukas EK, Sun F, Ho DW. Controller design for Markov jump systems subject to actuator saturation. Automatica. 2006; 42(3): 459-465.
- 22Zhou Y, Ma S, Kulan Z. H∞ control of continuous-time descriptor semi-Markov jump systems subject to actuator saturation. Paper presented at: Proceedings of the 36th Chinese Control Conference; July 26–28, 2017; Dalian, China.
- 23Hu Z, Mu X. Stabilization for switched stochastic systems with semi-Markovian switching signals and actuator saturation. Inf Sci. 2019; 483: 419-431.
- 24Ahn CK, Wu L, Shi P. Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica. 2016; 69: 356-363.
- 25Wu ZG, Park JH, Su H, Chu J. Non-fragile synchronisation control for complex networks with missing data. Int J Control. 2013; 86(3): 555-566.
- 26Yang GH, Wang JL. Non-fragile H∞ control for linear systems with multiplicative controller gain variations. Automatica. 2001; 37(5): 727-737.
- 27He S. Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls. Neurocomputing. 2015; 147(5): 350-357.
- 28Ma Y, Gu N, Zhang Q. Non-fragile robust H∞ control for uncertain discrete-time singular systems with time-varying delays. J Frankl Inst. 2014; 351(6): 3163-3181.
- 29Yue D, Tian E, Han QL. A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans Autom Control. 2013; 58(2): 475-481.
- 30Li F, Wu L, Shi P. Stochastic stability of semi-Markovian jump systems with mode-dependent delays. Int J Robust Nonlinear Control. 2014; 24: 3317-3330.
- 31Huang J, Shi Y. Stochastic stability and robust stabilization of semi-Markov jump linear systems. Int J Robust Nonlinear Control. 2013; 23: 2028-2043.
- 32Hu J, Wang Z, Gao H, Stergioulas LK. Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities. IEEE Trans Ind Electron. 2012; 59(7): 3008-3015.
- 33Xiong J, Lam J. Stabilization of networked control systems with a logic ZOH. IEEE Trans Autom Control. 2009; 54(2): 358-363.
- 34Xu L, Wang Q, Li W, Hou Y. Stability analysis and stabilisation of full-envelope networked flight control systems: switched system approach. IET Control Theory Appl. 2012; 6(2): 286-296.
- 35Zuo Z, Li Y, Wang Y, Li H. Event-triggered control for switched systems in the presence of actuator saturation. Int J Syst Sci. 2018; 49(7): 1478-1149.
- 36 Zhuang GM, Su SF, Xia JW, Sun W. HMM-based asynchronous H∞ filtering for fuzzy singular Markovian switching systems with retarded time-varying delays. IEEE Trans cybern. 202. https://doi.org/10.1109/TCYB.2020.2977127.
- 37 Zhuang GM, Xia JW, Feng J-E, Sun W, Zhang BY. Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat's lemma. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2020.2964057.
