The Study on D-stability of Dynamic Interval Systems Based on Robust State Observers

In this paper, we address the design problems of robust state observers for discrete-time dynamic interval systems with D-stability constrains. A method of designing the robust state observers is presented based on some matrix inequalities. It is not assumed that the system under consideration is necessarily regular and causal, the objective is to determine the observer gain matrix K such that the desired Robust Performance and Time-domain performance can be satisfied in the whole observe procedure and the closed-loop poles are placed in a specified disk while the regularity, causality and stability of the closed-loop system can be guaranteed for all admissible uncertainties, furthermore, the analytical expression of desired observer gain matrix K is also derived. Finally, a numerical example is given to demonstrate the application of the proposed method.