Output feedback control of discrete-time Lur'e systems through FIR Zames-Falb multipliers

• Main Authors: Bertolin, Ariádne L.J., Oliveira, Ricardo C.L.F., Valmorbida, Giorgio, Peres, Pedro L.D.
• Format: Conference Proceeding
• Language: English
• Subjects: Absolute stability; Discrete-time Lur'e systems; FIR Zames-Falb multipliers; Linear matrix inequalities; Output-feedback control
• ISSN: 2405-8963; 2405-8963
• DOI: 10.1016/j.ifacol.2023.10.252

This paper is concerned with output feedback control of discrete-time Lur'e systems with slope bounded nonlinearities that can be non-odd. Using FIR (Finite Impulse Response) Zames-Falb multipliers of any given order, stability conditions based on positive realness are proposed in terms of linear matrix inequalities and linear constraints that assure the ℓ1 norm bound for the multiplier. Importantly, the proposed approach does not require line searches. Applying a relaxation on the stability and exploiting the fact that the matrices of the system appear affinely in the conditions, an iterative method is constructed to search for the FIR Zames-Falb multiplier certifying stability. An extension to cope with the design of a control law is also presented, dealing with state or output feedback gains that may include a term proportional to the output of the nonlinear block. Numerical examples illustrate the advantages of the proposed approach, that can be numerically more efficient than other techniques from the literature.