H 2 and H ∞ digital redesign of analog controllers for continuous-time polytopic systems * * Supported by the Brazilian agencies CAPES, CNPq, FAPDF, and FAPESP (Proc. 2014/22881-1)

摘要

The aim of this paper is to investigate the problems of designing H ∞ and H 2 discrete-time stabilizing controllers for polytopic continuous-time systems through the digital redesign methodology. This technique consists of determining a stabilizing digital gain starting from a predetermined continuous-time controller, such that a performance criterion, associated to the difference between the continuous-time and discrete-time state trajectories, is minimized. In this paper, synthesis conditions are proposed in terms of parameter-dependent matrix inequalities with polynomial variables and a given scalar parameter. Differently from other approaches that minimize the Euclidean norm and can only handle precisely known systems, the proposed method minimizes a bound to the H 2 or H ∞ norm of a system that represents the dynamics of the error between the polytopic continuous-time plant and the discrete-time representation. Numerical examples are presented to show the advantages of the proposed methodology when compared with other conditions from the literature in the precisely known case, and to illustrate the applicability of the technique for uncertain systems.