Dynamic output-feedback control of continuous-time Lur'e systems using Zames-Falb multipliers by means of an LMI-based algorithm

This paper investigates the problems of stability analysis and control design for continuous-time Lur'e systems with slope bounded nonlinearities. Starting from a stability analysis condition from the literature, based on the real positivity and a bound to the L₁ norm of a certain transfer function, new sufficient conditions are proposed in an augmented parameter space for the simultaneous existence of a stabilizing dynamic output-feedback controller and a Zames-Falb multiplier certifying the closed-loop stability. The matrices of the controller realization as well as of the Zames-Falb multiplier appear affinely in the conditions, being dealt with as optimization variables. Furthermore, no line search is required to enforce the L₁ norm constraint. An iterative algorithm is constructed to solve the problem through semidefinite programming, providing dynamic controllers of any given order. The controller can take into account both the output of the linear part of the system and of the nonlinearity. Numerical examples illustrate the results.