Output variable structure control using Strictly Positive Real Systems

Abstract

The Strictly Positive Real (SPR) Systems have a great importance in the control of systems with uncertainties [1], [2], because of the important results available on the stability of these systems, for example, the Popov's asymptotic hiperstability [3]. This paper presents necessary and sufficient conditions to turn a Linear Time-Invariant System (LTIS) given by {A, B, C}, with more inputs than outputs, into a SPR, using only inputs and outputs measurements; these results are apllied in the VSS control. The system compensation is made by two static compensators, one of which forward feeds the inputs and the second back feeds the outputs of the plant. This result is useful in the control of systems with uncertainties using only the outputs; an application in the variable structure control with sliding modes, using only the outputs of the plant, without state observer or state filter is presented.