Control Strategies for Markov Jump Linear Systems
Summary
Markov Jump Linear Systems (MJLS) represent a class of stochastic dynamic models in which system parameters switch among a finite set of linear subsystems according to a Markov chain. Control strategies for MJLS must address abrupt regime changes, uncertainties in transition probabilities, time‐varying delays and external disturbances. A central theme is the construction of Lyapunov‐Krasovskii functionals that guarantee stochastic stability and performance indices such as H₂/H∞ norms or dissipativity measures. Controller synthesis often reduces to solving linear matrix inequalities (LMIs), enabling state‐feedback, static or dynamic output‐feedback designs under polytopic uncertainties. Event‐triggered schemes and asynchronous protocols have emerged to reduce communication load, employing hidden Markov models to manage partial mode information. Adaptive and fault‐tolerant approaches compensate for actuator faults and unmodelled dynamics, while fuzzy logic frameworks handle nonlinearity and unknown transition rates. These strategies find applications in networked control, robotic arms, vehicle suspension and power systems, where robustness and efficient resource utilisation are paramount.
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Control Strategies for Markov Jump Linear Systems publication trend
The graph below shows the total number of articles in control strategies for markov jump linear systems across all publications each year (not limited to Nature Index journals).
Technical terms
Markov Jump Linear System (MJLS): A linear system whose parameters switch among discrete modes according to a Markov chain.
Lyapunov‐Krasovskii Functional: A scalar functional used to assess stability of time‐delay or switched systems.
Linear Matrix Inequality (LMI): A convex constraint on matrix variables that enables efficient controller synthesis.
H∞ Control: A robust control method that minimises the worst‐case gain from disturbance to output.
Event‐Triggered Control: A strategy that reduces communication by updating controllers only when a specified condition is met.
Hidden Markov Model (HMM): A statistical model for systems with unobservable (hidden) mode transitions.
References
- An Improved Fuzzy Event-Triggered Asynchronous Dissipative Control to TS FMJSs With Nonperiodic Sampled Data. IEEE Transactions on Fuzzy Systems (2020).
- Zonotope-Based Asynchronous Fault Detection for Markov Jump Systems Subject to Deception Attacks via Dynamic Event-Triggered Communication. IEEE Open Journal of the Industrial Electronics Society (2022).
- Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties. Mathematics (2022).
- Co-Design of Event-Triggered Scheme and H∞ Output Control for Markov Jump Systems Against Deception Attacks. IEEE Access (2020).
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