Abstract
This paper considers linear time-invariant continuous-time control systems with saturation and/or dead-zone nonlinearities, and proposes two synthesis methods satisfying a regional L2 and/or exponential stability performance for the system based on the generalized sector approach. One of them is an integrated design of dynamical output feedback and anti-windup controllers, while the other is an integrated design of static output and state feedback controllers. The two methods assume the output of the nonlinearities to beavailable for the control. In this case, this paper indicates that the synthesis problems using the two methods can be recast as linear matrix inequality (LMI) optimization problems, respectively. Furthermore, it is proved that the synthesis condition based on the former dynamical controller is a sufficient condition of the corresponding one based on the latter static controller. In the special case of the same class of the two controller input signals, it is also proved that two achievable control performances using the two controllers are exactly the same. In particular, it is clarified that the synthesis condition using the dynamical controller is composed of a synthesis condition of a state feedback gain for control systems with saturation and/or dead-zone nonlinearities, and a synthesis condition of an observer gain for linear control systems without the nonlinearities. Finally, this paper points out that the proposed synthesis method is helpful through numerical examples designing control systems with anti-windup control structures via the derived LMI conditions.
