scholarly journals Stabilization of Regime-Switching Processes by Feedback Control Based on Discrete Time Observations II: State-Dependent Case

2019 ◽  
Vol 57 (2) ◽  
pp. 1413-1439
Author(s):  
Jinghai Shao ◽  
Fubao Xi
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Regime Switching ◽  
Dependent Case ◽  
State Dependent ◽  
Discrete Time Observations

Feedback control based on discrete-time state observations for stabilization of coupled regime-switching jump diffusion with Markov switching topologies

2020 ◽  
Vol 37 (4) ◽  
pp. 1423-1446
Author(s):  
Yongbao Wu ◽  
Haotian Pi ◽  
Wenxue Li
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Regime Switching ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Jump Diffusion ◽  
Switching Topologies ◽  
Directed Spanning Tree ◽  
Strongly Connected ◽  
Discrete Time Observations

Abstract In this paper, the stabilization of coupled regime-switching jump diffusion with Markov switching topologies (CRJDM) is discussed. Particularly, we remove the restrictions that each of the switching subnetwork topologies is strongly connected or contains a directed spanning tree. Furthermore, a feedback control based on discrete-time state observations is proposed to make the CRJDM asymptotically stable. In most existing literature, feedback control only depends on discrete-time observations of state processes, while switching processes are observed continuously. Different from previous literature, feedback control depends on discrete-time observations of state processes as well as switching processes in this paper. Meanwhile, based on graph theory, stationary distribution of switching processes and Lyapunov method, some sufficient conditions are deduced to ensure the asymptotic stability of CRJDM. By applying the theoretical results to second-order oscillators with Markov switching topologies, a stability criterion is obtained. Finally, the effectiveness of the results is illustrated by a numerical example.

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