An LMI approach with improved numerical efficiency for the quadratic stabilization of a class of linear uncertain systems

The purpose of this paper is to provide a numerically efficient method for the quadratic stabilization of a class of linear, discrete-time, uncertain, time-varying systems. The considered class of systems is characterized by an interval time-varying (ITV) matrix and constant sensor and actuator matrices. It is required to find a linear time-invariant (LTI) static output feedback controller yielding a quadratically stable closed-loop system independently of the parameter variation rate. The solvability conditions are stated in terms of LMIs. The set of LMIs includes the stability conditions for the feedback connection of a unique suitably defined extreme plant with a LTI output controller and the positivity of a closed-loop extremal matrix. A consequent noticeable feature of the paper is that the total number of LMIs is independent of the number of uncertain parameters. This greatly enhances the numerical efficiency of the design procedure.