Stability Synthesis with Reduced-order Output Feedback/Anti-windup Controllers

—Relation between Controller Order and Control Performance

Abstract

This paper considers linear time-invariant continuous-time systems with control input saturation nonlinearities, and proposes two regional stability synthesis methods of output feedback controllers such as an ellipsoid defined by a level set of a quadratic Lyapunov function to be a domain of attraction for the systems based on the generalized sector approach. One of them is an integrated design of full-order dynamical output feedback and anti-windup controllers with the same plant order, while the other is an integrated design of reduced-order dynamical output feedback and antiwindup controllers to be less than the number of available plant states from the plant order. The two methods assume the output of the nonlinearities to be available 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 two subsets of achievable domains of attraction using the two controllers are exactly the same. Thus this paper concludes that the reduced-order controller does not decrease the size of the achievable domain of attraction, within our framework, when compared with that resulting from the full-order controller.