An LMI approach to design interval observers for discrete-time linear switched systems

This paper presents simple design methods of interval observers for discrete-time linear switched systems in the presence of output noise and system perturbation. The interval observers are designed using the internal positivity of the system without need to a coordinate transformation. This approach is proposed for arbitrary switching signals and it can be generalized to dwell-time switching rules. The observation gain that guarantees both stability and positivity of the interval estimate errors is synthesized by solving a Linear Matrix Inequality (LMI) feasibility problem. The theoretical result is supported by numerical simulations.