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Resilient linear filtering of uncertain systems. (English) Zbl 1162.93403
The objective of the paper is to contribute to the further development of resilient linear filtering for a class of continuous-time systems with norm-bounded uncertainties. The term “resilient” means robustness with respect to plant parametric uncertainties and against gain perturbations in filter matrices. A class of resilient linear filters with additive filter gain perturbations is described. The perturbations are supposed to be present in both the estimator gain and dynamic matrices. The design problem of robust resilient filtering is formulated as a problem of convex optimization over linear matrix inequalities (LMIs). An important special case with resilient linear filter and additive gain perturbations is considered, which recovers, in the nominal case, previously known filtering results. By a limiting approach, an LMI result on resilient Kalman filter is derived and finally, it is demonstrated that the case of multiplicative filter gain perturbations can be developed conveniently as an extension of the forgoing results. An example illustrates the theoretical developments.
MSC:
93E11Filtering in stochastic control
93D09Robust stability of control systems