Robust energy-to-peak filter design for stochastic time-delay systems

This paper considers the robust energy-to-peak filtering problem for uncertain stochastic time-delay systems. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time-varying. Attention is focused on the design of full-order and reduced-order filters guaranteeing a prescribed energy-to-peak performance for the filtering error system. Sufficient conditions are formulated in terms of linear matrix inequalities (LMIs), and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. In addition, the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, have been taken into consideration, with convex optimization problems obtained for the design of desired robust energy-to-peak filters.