On the design of fixed-order output controllers for 2D systems via complex Lyapunov functions

This paper addresses the problem of designing fixed-order output stabilizing controllers for 2D systems with homogeneous or mixed dynamics. A strategy is proposed by searching for a complex Lyapunov function depending polynomially on a frequency and on the controller. The strategy consists of determining the controller candidate in a chosen region that maximizes the feasibility of the Lyapunov inequalities. This is realized by solving two semidefinite programs, the first one for constructing a feasibility index, and the second one for constructing the controller that achieves its maximum.