Paper Info
Title
Stabilization and Optimization of Discrete-Time Markovian Jump Linear Systems via Mode Feedback Control
Abstract
This article is devoted to a specific kind of discrete-time switched linear systems, where the switching signal is governed by a Markov chain, i.e., Markovian jump linear systems. For such systems, a mode feedback control mechanism is adopted to adjust the mode transition probability matrix, which is referred to as the switching law design, and the optimal mode feedback controller is sought to minimize a quadratic performance index containing both the system state and the mode feedback control input. First, the admissible set of the mode feedback control is investigated, and a sufficient condition is derived to ensure the desired stochastic stability. Second, under the assumption that the concerned system is mode-cost sequential, the original performance index is approximated into a new tractable one and a suboptimal mode feedback controller is then derived within the admissible set. Third, we consider a general situation where no specific requirements are imposed on the Markovian jump linear systems’ dynamics, derive the optimal mode feedback controller via a value-iteration-based algorithm, and prove the convergence of the obtained optimal controller. Finally, simulation results are provided to illustrate the validity of the proposed mode feedback control mechanism.
Year
DOI
Venue
2022
10.1109/TAC.2021.3131547
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Discrete-time Markovian jump linear systems (MJLSs),mode feedback control,quadratic performance index,stochastic stability
Journal
67
Issue
ISSN
Citations 
12
0018-9286
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Jin Zhu130.74
Kai Xia200.34
Qiang Ling325137.43
Wei Chen410438.74
Geir Dullerud514918.72