Robust H∞ filtering for uncertain linear systems with multiple time-varying state delays: an LMI approach

The problem of guaranteed cost H_∞ filtering for continuous-time uncertain linear systems with multiple time-varying state delays is investigated. The uncertain parameters are supposed to belong to convex bounded domains (polytope type uncertainty). The aim is to determine a stable linear filter which assures stability and a prescribed H_∞ noise attenuation level for the filtering error system irrespective of the uncertainties. Using a Lyapunov-Krasovskii approach, sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities, which can be efficiently solved by means of powerful convex programming tools with global convergence assured. An example illustrates the proposed filter design