Robust Recursive Regulator for Polytopic Markovian Jump Linear Systems With Random State Delays

• Published in: IEEE transactions on automatic control Vol. 69; no. 12; pp. 8916 - 8923
• Main Authors: Odorico, Elizandra Karla, Bueno, Jose Nuno A. D., Terra, Marco H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Apexes; Control stability; Control systems; Control theory; Cost function; Delay; Delays; Discrete-time systems; Dynamical systems; Feedback control; Linear systems; Markov chains; Markov jump linear system (MJLS); Mathematical models; Optimal control; polytopic uncertainties; Real time; Regulation; Regulators; Riccati equation; Riccati equations; Robust control; Stability analysis; State feedback; state time-delay; Time varying control; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3423568

The control problem of dynamic systems that undergo sudden changes and rely on past data is known to be challenging to solve and has received a lot of attention in the past years. Meanwhile, the optimal control theory has been widely used to develop efficient conditions for stability analysis and control synthesis. In this article, we propose a robust regulation strategy for Markovian jump linear systems subject to delayed states and polytopic uncertainties. The time-varying delay belongs to a known interval. To obtain less conservative results, we consider the maximum variation rate of the delay. We apply the augmented system approach and model the delay by a Markov chain, obtaining a delay-free Markovian system. Then, we establish a min-max optimization problem whose quadratic cost function collectively weights all the polytope vertices through a penalty parameter. The solution yields a mode-dependent state-feedback control law. Unlike most approaches in the literature, the main features of the proposed method are its recursiveness and stability conditions, which can be achieved through the Riccati equations. They are suitable for embedded and real-time applications. We illustrate the potential and effectiveness of the proposed regulator one numerical examples.