Reduced-order controllers for the continuous-time H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the continuous-time H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents new controller degree bounds for the H_∞ control problem, and provides new solutions to designing reduced-order controllers for the H_∞ control problem with invariant zeros in the closed right half complex plane. When such unstable invariant zero exists (even it is an imaginary-axis zero), this paper shows that reduced-order controllers with order strictly less than the generalized plant order exist if the H_∞ control problem is solvable. Moreover, LMI based methods for constructing the reduced-order controllers are given.