Proportional integral observer using disturbance attenuation strategy for discrete-time linear singularly perturbed system

This paper deals with the observability bound problem of a discrete-time linear singularly perturbed system (DTLSPS) subject to L2 disturbance and L2 noise. A proper PI observer, known by its robustness, is devised for state estimation, ensuring that the observation error is asymptotically stable and satisfies the H∞ performance constraint for a proper bound of the singular perturbation parameter based on a quadratic Lyapunov function and the H∞ norm. In order to design this observer, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are developed to ensure the robust stability bound of the considered system. This task is also achieved using a quadratic Lyapunov function and the H∞ norm. Then, using the outcomes of these two tasks, the observability bound of the system is determined. Two simulation examples are then given to validate the proposed strategy.