Robust Controller Synthesis under Markovian Mode Switching with Periodic LTV Dynamics

TL;DR

This paper develops LMI-based methods for designing controllers for periodically time-varying Markov-jump linear systems, ensuring stability and optimizing performance under mode switching.

Contribution

It introduces novel stability conditions and controller synthesis frameworks that handle periodic LTV dynamics with Markovian mode switching.

Findings

Controllers guarantee mean square stability.

Frameworks optimize quadratic cost and region of attraction.

Numerical simulations confirm stability and fault-tolerance.

Abstract

In this work, we propose novel LMI-based controller synthesis frameworks for periodically time-varying Markov-jump linear systems. We first discuss the necessary conditions for mean square stability and derive Lyapunov-like conditions for stability assurance. To relax strict stability requirements, we introduce a new criterion that doesn't require the Lyapunov function to decrease at each time step. Further, we incorporate these stability theorems in LMI-based controller synthesis frameworks while considering two separate problems: minimizing a quadratic cost, and maximizing the region of attraction. Numerical simulations verify the controllers' stability and showcase its applicability to fault-tolerant control.