Control Design for One Class of Uncertain Metzler-Takagi-Sugeno Time-Delay Systems

Abstract

This paper presents a new approach to synthesize the control for one class of uncertain Metzler-Takagi-Sugeno time-delay systems. The structural parametric constraints of the closed-loop system, their diagonal matrix representations as well as the interval system parameter bounds are accounted into an associated set of the linear matrix inequalities. After sorting out the relevant preliminaries in the uncertain structure of the Metzler systems and the specific properties of the time-delay positive system representations, the design conditions reflecting quadratic system stability of the considered system class are proven in the matrix inequality framework. The main result of the control law parameter design is shown in detail by the numerical example in order to characterize potential adaptation of the method for purely Metzler matrix parameter structures.