ℋ∞Filter Design with Minimum Entropy for Continuous-Time Linear Systems

Abstract

We deal with the design problem of minimum entropyℋ∞filter in terms of linear matrix inequality (LMI) approach for linear continuous-time systems with a state-space model subject to parameter uncertainty that belongs to a given convex bounded polyhedral domain. Given a stable uncertain linear system, our attention is focused on the design of full-order and reduced-order robust minimum entropyℋ∞filters, which guarantee the filtering error system to be asymptotically stable and are required to minimize the filtering error system entropy (ats0=∞) and to satisfy a prescribedℋ∞disturbance attenuation performance. Sufficient conditions for the existence of desired full-order and reduced-order filters are established in terms of LMIs, respectively, and the corresponding filter synthesis is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.