In this work, we analyze the instability of continuous-time Markov jump linear systems. Although there exist several effective criteria for the stability of Markov jump linear systems, there is a lack of methodologies for verifying their instability. We present a novel criterion for the exponential mean instability of Markov jump linear systems. The main tool of our analysis is an auxiliary Markov jump linear system, which results from taking the Kronecker products of the given system matrices and a set of appropriate matrix weights. We show that the problem of finding matrix weights for tighter instability analysis can be transformed to the spectral optimization problem on an affine matrix family, which can be efficiently solved by gradient-based non-smooth optimization algorithms. Besides, we study state-feedback control of Markov jump linear systems with state and mode-observation delays. Our formulation provides a novel framework to analyze and design feedback control laws for Markov jump linear systems with state and mode-observation delays. We present a procedure to transform the closed-loop system with delays into a Markov jump linear system. Moreover, based on this transformation, we propose a set of Linear Matrix Inequalities (LMI) to design feedback gain for stabilization and mixed H2/H∞ control.
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