Proportional-delayed controllers design for LTI-systems a geometric approach

Abstract : This paper focuses on the design of non-fragile P-controllers for single-input-single-output (SISO) linear time-invariant (LTI) systems. The basis of this work is a geometric approach allowing to partitioning the parameter-space in regions with constant number of unstable roots. This methodology defines the hyperplanes separating the aforementioned regions and characterizes the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find non-fragile P-gains ensuring the stability of the LTI system under consideration. More precisely, in this work a simple geometric-based algorithm is derived in order to propose a non-fragile P-controller. Several numerical examples illustrate the e↵ectiveness of the proposed approach.