Component-wise bounds for uncertain MIMO control systems with finite level quantizers

This work presents a methodology that guarantees component-wise stability bounds for the states of a disturbed linear Multiple Input Multiple Output (MIMO) feedback control systems, featuring bounded uncertainties and bounded quantization errors both in the measurements and in the controls. The controller synthesis is based on the design of a robust invariant ellipsoidal set, which assumes that all the uncertainties sources introduce upper bounded signals. We show that the component-wise boundedness requirements for the states and controls of the closed loop uncertain system can be expressed as a Linear Matrix Inequality (LMI) problem. Thus, feasibility and optimal controller design can be effectively and advantageously computed solving a convex linear optimization problem. The approach is validated by means of a meaningful numerical example.