H<inf>∞</inf> filter design for discrete-time system with lossy measurement: An LMI approach

Abstract

This paper investigates the problem of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> full-order filter and reduced-order filter design for a class of discrete-time system with lossy measurement. The lossy measurement is described by a binary switching sequence satisfying Bernoulli distribution. By introducing slack variable, sufficient conditions are obtained for the existence of admissible filters. Moreover, in order to overcome the non-convex constraint for reduced-order H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter design, by converting the structural constraints on the Lyapunov matrix to the constraints on the slack variables, the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities(LMIs), which can be solved via efficient interior-point algorithms. Numerical example is presented to illustrate the feasibility and advantages of the proposed methodologies.