Multiobjective filtering for nonlinear time-delay systems with nonzero initial conditions based on convex optimizations

A multiobjective filtering problem is investigated for a class of continuous-time time-delay systems with nonzero initial conditions. The plant is supposed to have nonlinear dynamics and multiple time delays in both the state and the measured output. In order to address the compatible mixed H-2 and H-infinity performance measure for the filtering problem, the generalized H-infinity performance index is introduced instead of the standard one. The novel mixed H-2 and H-infinity filtering problem is formulated as an optimization problem, where the solvability conditions are provided via convex computation approaches. After some algebraic transformations and decompositions, the involved nonlinear constraints can be eliminated and linear matrix inequality-based convex algorithms can be given for the filter design. A simple example is given to illustrate the optimization algorithms.