On the Design of Interval Observers for Discrete-Time Linear Switched Systems without Using Similarity Transformations

This paper presents synthesis methods of Interval Observers (IO) for discrete-time linear switched systems subject to additive unknown-but-bounded process and measurement noises. The novelty of the proposed methods consists in the designing of IO directly in the original state coordinates of the systems. This enables to: (i) mitigating the wrapping effect related to the classical use of similarity transformations; (ii) avoiding the impulsive behavior of the estimation error dynamics, mostly generated by the use of different similarity transformation for each mode of the switched system; (iii) reducing online computational effort. In addition, Bilinear Matrix Inequalities (BMI) and Linear Matrix Inequalities (LMI) conditions are established to check the existence and to compute stabilizing observer gains. The obtained theoretical results are supported by numerical simulations.