Robust PI Multiobserver for Discrete Nonlinear Singularly Perturbed System

This paper deals with the observability bound problem of a discrete-time nonlinear singularly perturbed systems (SPSs) subject to \(\mathcal {L}_2\) disturbances. The considered system is represented by a coupled state multimodel (MM). A \({H_\infty }\) proportional-integral (PIMO), features by its robustness, is designed, ensuring that the state estimation error is asymptotically stable and satisfies the \({H_\infty }\) performance constraint for a proper bound of the singular perturbation parameter based on a quadratic Lyapunov function and the \({H_\infty }\) norm. Before designing this observer, a sufficient conditions described in terms of linear matrix inequalities (LMIs) are developed to ensure the robust stability bound of the considered system. Then, using the results of these two tasks, the observability bound of the system is determined.