Stability and performance preserving controller order reduction via Youla parameterization and LMIS

This paper develops a stability and performance preserving controller order reduction method for linear time-invariant continuous-time single-input, single-output systems. In this method, the error between the complementary sensitivity functions of the nominal closed-loop system and closed-loop system using the reduced-order controller is converted to a frequency-weighted error between the Youla parameters of the full-order and reduced-order controllers and then the H_∞ norm of this error, subject to a set of linear matrix inequality constraints, is minimized. The main ideas of order reduction and stability preservation are contained in the constraints of the optimization problem. However, since this minimization problem is nonconvex, the Youla parameter of the reduced-order controller is obtained by solving a suboptimal linear matrix inequality problem, that is convex and readily solved using existing semi-definite programming solvers. It is shown that the resulting reduced-order controller preserves the stability and performance of the nominal closed-loop system in disturbance rejection and input tracking.