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Multiobjective filtering for nonlinear time-delay systems with nonzero initial conditions based on convex optimization. (English) Zbl 1106.93052
Summary: 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 $H_{\infty}$ performance measure for the filtering problem, the generalized $H_{\infty}$ performance index is introduced instead of the standard one. The novel mixed $H_{2}$ and $H_{\infty}$ 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.

##### MSC:
 93E11 Filtering in stochastic control 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 93C41 Control problems with incomplete information 90C25 Convex programming
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