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arXiv · 2409.11537

Robust Controller Synthesis under Markovian Mode Switching with Periodic LTV Dynamics

Shaurya Shrivastava·Kenshiro Oguri
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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.

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Shaurya Shrivastava, Kenshiro Oguri. 2024-09-17. Robust Controller Synthesis under Markovian Mode Switching with Periodic LTV Dynamics. https://arxiv.org/abs/2409.11537

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