Further study on stability analysis for Markov linear parameter-varying systems

This article addresses the problem of stability analysis for a class of Markov jump systems with time-varying parameters. Unlike previous studies that assumed a bounded rate of parameter variation, this research allows for an arbitrary parameter variation rate. Additionally, a new parameter-dependent homogeneous polynomial Lyapunov function is designed, which depends on both the Markov process and time-varying parameters simultaneously. The switching approach is employed to deal with the derivatives of time-varying parameters, while the average dwell time (ADT) approach is utilized to handle the switching signal. Thus, a less conservative stability criterion is obtained to ensure the exponentially mean-square stability of the system. Three examples are provided to verify the effectiveness of the obtained results.