A generalized nonlinear H_∞ filter design for discrete-time Lipschitz descriptor systems

This paper is devoted to the H_∞ filtering problem for nonlinear discrete-time descriptor systems subject to Lipschitz condition. The objective is to design a generalized nonlinear full-order filter, such that the resulting filtering error system is admissible (regular, causal, and asymptotically stable), while a prescribed H_∞ disturbance attenuation level is satisfied. By using the Lyapunov stability theorem and the slack matrix approach, a new less conservative sufficient condition for the regularity, causality, and stability of the considered system is derived, which can also ensure that the studied nonlinear discrete-time singular system has a unique solution. Based on this condition, a sufficient LMI-based condition for the existence of the desired H_∞ full-order filter is derived to guarantee that the filtering error system is admissible while satisfying a given H_∞ performance index. Further, the nonlinear filter design method is proposed, and by solving a linear matrix inequality (LMI), the explicit expression of the desired filter gain matrices is also given. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.