TY - JOUR
T1 - H∞ control for continuous-time Markov jump nonlinear systems with piecewise-affine approximation
AU - Zhu, Yanzheng
AU - Xu, Nuo
AU - Chen, Xinkai
AU - Zheng, Wei Xing
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under Grant U1813201 and Grant 61973131 , in part by the Japan Society for the Promotion of Science under Grant 21K04129 , in part by the Fujian Outstanding Youth Science Fund, China under Grant 2020J06022 , and in part by the Scientific Research Funds of Huaqiao University, China under Grant 60550Y19010 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Michael V. Basin under the direction of Editor Ian R. Petersen.
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2022/7
Y1 - 2022/7
N2 - This paper investigates the problem of stability, H∞ performance analysis, and H∞ control for continuous-time Markov jump nonlinear systems, where the nonlinear subsystems are approximated by the piecewise-affine technique. The proposed Markov jump piecewise-affine systems contain different modes and regions, both of which are determined by Markov chains and piecewise-affine partitions, respectively. A new admissible adjacent region switching paths (AARSPs) algorithm is proposed for the first time in the continuous-time domain to decrease the conservatism of the complete adjacent region switching paths (CARSPs) algorithm. This new algorithm optimizes the path selection conditions of the next instantaneous time region switching in the CARSPs algorithm, and effectively reduces the computational complexity and the conservatism of the CARSPs algorithm. Furthermore, a state-feedback piecewise-linear controller is designed by means of the ellipsoidal outer approximation estimation method, such that the corresponding closed-loop system is stochastically stable and has a guaranteed H∞ performance index. Finally, the effectiveness and practicability of both the AARSPs algorithm and the piecewise-linear control strategy are fully demonstrated via two illustrative examples including a class of tunnel diode circuit systems.
AB - This paper investigates the problem of stability, H∞ performance analysis, and H∞ control for continuous-time Markov jump nonlinear systems, where the nonlinear subsystems are approximated by the piecewise-affine technique. The proposed Markov jump piecewise-affine systems contain different modes and regions, both of which are determined by Markov chains and piecewise-affine partitions, respectively. A new admissible adjacent region switching paths (AARSPs) algorithm is proposed for the first time in the continuous-time domain to decrease the conservatism of the complete adjacent region switching paths (CARSPs) algorithm. This new algorithm optimizes the path selection conditions of the next instantaneous time region switching in the CARSPs algorithm, and effectively reduces the computational complexity and the conservatism of the CARSPs algorithm. Furthermore, a state-feedback piecewise-linear controller is designed by means of the ellipsoidal outer approximation estimation method, such that the corresponding closed-loop system is stochastically stable and has a guaranteed H∞ performance index. Finally, the effectiveness and practicability of both the AARSPs algorithm and the piecewise-linear control strategy are fully demonstrated via two illustrative examples including a class of tunnel diode circuit systems.
KW - Admissible adjacent region switching paths
KW - H control
KW - Markov jump piecewise-affine systems
KW - Piecewise-linear controller
KW - Tunnel diode circuit system
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U2 - 10.1016/j.automatica.2022.110300
DO - 10.1016/j.automatica.2022.110300
M3 - Article
AN - SCOPUS:85129319306
SN - 0005-1098
VL - 141
JO - Automatica
JF - Automatica
M1 - 110300
ER -