Reference model tracking for Markovian jump linear systems with partially unknown transition rates

Abstract

This work investigates the tracking problem for a Markovian Jump Linear Systems (MJLS) with partially unknown transition rates (TR), focusing on the design of a control strategy to follow a deterministic reference model. To ensure stability and accurate tracking, the control problem is reformulated using augmented system dynamics. A state-feedback control strategy is developed via the Linear Matrix Inequality (LMI) framework. This structured approach guarantees system stability and enables the MJLS to follow the desired reference trajectory. Further, stability was maintained under external disturbances applied to the system, demonstrating the robustness of the approach even with partially unknown transition rates.