On the use of multi-loop circle criterion for saturating control synthesis

This paper is concerned with regional stabilization of linear time-invarian t systems by dynamic output feedback controllers subject to known bounds on the magnitudes of the control inputs. Specifically, we consider the achiev able region of attraction, i.e. the set of vectors with the following prope rty: There exists a (nonlinear) controller such that any closed-loop state trajectory converges to the origin as long as the initial state belongs the set. Two subsets of such set are characterized. One is derived from the li near analysis that considers the behavior of the states in the linear (non- saturated) region only, while the other is based on the nonlinear analysis using the multi-leap circle criterion. The main result of this paper shows that the two sets are exactly the same. Thus we conclude that the circle cr iterion does not help, within our framework, to increase the size of the re gion of attraction in saturating control synthesis when compared with that resulting from the linear analysis. (C) 2000 Elsevier Science B.V. All righ ts reserved.