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Stability and implementable ${ℍ}_{\infty }$ filters for singular systems with nonlinear perturbations. (English) Zbl 1176.93075
Summary: We investigate the problem of designing ${ℍ}_{\infty }$ filter for a class of continuous-time uncertain singular systems with nonlinear perturbations, which can be realized in practice. The perturbation is a time-varying function of the system state and satisfies a Lipschitz constraint. The design objective is to guarantee that a prescribed upper bound on an ${ℍ}_{\infty }$ performance of the robust filter is attained for all possible energy-bounded input disturbances and all admissible uncertainties and which can be implemented on-line to get a good replica of the state. We first establish sufficient condition for the existence and uniqueness of solution to the singular system connected with the normal filter. Using a linear matrix inequality (LMI) format, we then provide a sufficient condition for the asymptotic stability of the realizable ${ℍ}_{\infty }$ filter. Then by means of a convex analysis procedure the filter gain matrices are derived and an important special case is readily deduced. Finally, a numerical example is presented to illustrate the theoretical developments.
##### MSC:
 93E11 Filtering in stochastic control 93B36 ${H}^{\infty }$-control
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