On the H-2 Control of Hidden Markov Jump Linear Systems

This letter studies H-2 control of linear systems with parameters driven by a hidden Markov chain, emphasizing a property of invariance of the norm to time shifts in the disturbance signal, which we call H-2 time-invariance (H2TI). We show that some systems are not H2TI and that the lack of H2TI may deteriorate the performance of H2 control systems when they are subject to disturbances other than impulses at the time instant k = 0 (as in standard H-2 control). This motivates us to propose a new variant of the H-2-norm, based on a stochastic process having an impulse at a random time. We develop the formula for computing this new variant and apply the result to an LMI optimization problem. Numerical tests are performed, indicating the superiority of the proposed controller for systems subject to different types of disturbances.