Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities
By Lixian Zhang, El Kebir Boukas, James Lam. IEEE Transactions on Automatic Control, 2008
495 citations recorded by the source corpus.
In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.
Subfields: Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/164129d9145ed934669156ac832e39bbeae407e7
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Citations in the corpus
- Stochastic stability and robust stabilization of semi‐Markov jump linear systems (2013, unknown): “For instance, the stability analysis, filter and control design problems were investigated in [11–13], and the optimal control and filter design for MJLSs were discussed in [14–16].”
- Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks (2013, background): “Accordingly, the problems of uncertain TPs and partially unknown TPs have been addressed in [23] and [27], respectively.”
- Attitude Tracking of Rigid Spacecraft With Bounded Disturbances (2011, background): “In most literature works, for unknown disturbances, control design schemes can only achieve disturbance attenuation [12]–[14].”
- Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays (2011, background): “Generally speaking, for some practical systems, the transition probabilities of the Markov chain we get will never be precise, i.e., some elements in transition probability matrix are unknown [ 41 ].”
- Passivity-Based Asynchronous Control for Markov Jump Systems (2017, background): “When both the Markov jump parameters and time delays appear in the systems, the problems of stability and stabilization have been studied in [7]–[9].”
- A survey on Markovian jump systems: Modeling and design (2015, background): “In [50-52], the transition rates or probabilities of the jump are considered to be partially accessed, i.”
- New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information (2014, methodology): “Remark 1 In comparison with some existing results on stability and performance analysis for MJLSs [5,7,9,19], the results given in Theorem 1 have some merits.”
- Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters (2011, background): “Digital Object Identifier 10.1109/TCSI.2011.2106090 [6], and [ 16 ], respectively.”
- Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions (2010, background): “To relax the assumption that all the TPs are known, a new concept for MJLSs with partially unknown TPs is proposed [15] and a series of studies have been carried out [16]–[18].”