Finite-horizon Robust H∞ filter design for discrete systems with convex polytopic uncertainty

The paper addresses the finite-horizon robust H_∞ filtering for discrete-time systems with convex polytopic uncertainty. A sufficient condition for the existence of finite-horizon robust H_∞ filtering is presented by parameter-dependent Lyapunov function method with LMI approach. Two slack variable matrixs with special structure are introduced to design the finite-horizon robust H_∞ filter. The resulting filter can satisfy the given performance index for all admissible uncertainties. Finally, a numeric simulation shows the filter obtained achieves the specified design goal.