Abstract
This paper proposes analysis and synthesis method for the set of initial state vectors of saturating control systems such that any closed-loop state trajectory is bounded for all time and L2 norm of the performance signal is less than a prescribed level. We treat linear time-invariant systems with dynamic output feedback controllers subject to known bounds on the magnitudes of the control inputs. We assume that the initial state vectors belong to the bounded set and disturbance inputs belong to a set of signals having bounded L2 norm. Two subsets of such achievable set of initial state vectors are characterized. One is derived from the linear 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-loop circle criterion. We can show that the two sets are exactly the same in the synthesis case. Thus we conclude that the circle criterion does not help, within our framework, to increase the size of the initial state space region in saturating L2 performance synthesis when compared with that resulting from the linear analysis.
