| Abstrakt: |
In this paper, we address the control problem of Markov jump linear systems with multiplicative noise and partial observations of the Markov chain (operating mode). We devise a new approach for H2 analysis and control in a scenario of fast switching mode detectors, which considers the limiting case in which the switching frequency of the detector tends to infinity. Besides the interest in its own right, the approach devised here is particularly interesting in situations in which the mode estimates are updated continuously in time and subject to ambiguity, and therefore will typically change much faster than the actual operating mode. This strategy allows for a considerable reduction of the cardinality of the Markov chain's state space, and homogenizes the large transition parameters that correspond to the fast transitions. Therefore, it leads us to better-conditioned computational problems of reduced dimensionality, in comparison to the existing detector-based designs. A great deal of the existing literature on singularly perturbed switching diffusions relies on weak convergence methods. Our approach starts from a novel point of view, which hinges on pointwise convergence of a certain semigroup operator as the very underpinning technique of this paper. This strategy enables us to, in the fast-switching limit case, analyze mean square stability and homogenized H2 performance through operator theory. We also introduce a new method for the H2 design of homogenized controllers via linear matrix inequalities (LMIs), and show, in a numerical example, that it can yield better results than an existing approach from the recent literature. [ABSTRACT FROM AUTHOR] |
