Robust filter design for a class of uncertain systems with D stability constraints under a unified framework

Based on a new performance index, the problem of filter design for a class of continuous-time uncertain systems with state-dependent uncertainties is investigated in this paper, taking into account the D stability constraints. Attention is focused on solving the H_∞, L₂−L_∞, passive and dissipative robust filter design problems for such systems with D stability constraints in a unified framework by using the novel performance index. Through employing the Lyapunov stability theory, the feasibility criteria for analysis of robust disturbance attenuation performance are derived first. Furthermore, the linear matrix inequalities (LMIs)-based approach for the design of model-independent filters of the considered systems is developed such that the corresponding filtering error system guarantees the prescribed H_∞, L₂−L_∞, passive and dissipative performance indices with D stability constraints. It is particularly worth mentioning that the model-independent filter proposed in this paper does not require the model information is accessible for the filter design. Finally, a numerical example of tunnel diode circuit system is provided to demonstrate the applicability and effectiveness of the proposed robust filter design method.