Reduced-order energy-to-peak filtering for hidden Markov jump linear systems

Abstract

This paper deals with the design of a energy-to-peak (also known as ℓ2/ℓ∞) reduced-order filter for discrete-time Markov jump linear systems assuming that the filter has only access to an estimation of the Markov parameter, coming from the output of a detector device. To model this situation we consider that the process consisting of the Markov chain and the detector signal is a hidden Markov process. The main result shows that, by fixing the filter’s order to n^, if a set of linear matrix inequalities (LMI) holds true, then we can design a filter of order n^, which depends only on the estimation of the Markov parameter, such that an upper bound for the ℓ2/ℓ∞ ratio between the output peak norm value and the ℓ2 norm of an external disturbance is satisfied. It is also shown that our approach encompasses the case of networked-induced delay systems with imperfect measurement of the delay variable, and the robust polytopic case, with uncertainties on the Markov transition probabilities and detection probabilities. The paper is concluded with an illustrative example using the available computational LMI package tools.