Output feedback control of saturated discrete-time linear systems using parameter-dependent Lyapunov functions

• Published in: Systems & control letters Vol. 57; no. 11; pp. 896 - 903
• Main Authors: Zheng, Qian, Wu, Fen
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2008; Elsevier
• Subjects: Actuator saturation; Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Domain of attraction; Exact sciences and technology; Output feedback control; Parameter-dependent Lyapunov function; Restricted [formula omitted] gain; Domain of attraction; Restricted ℓ 2 gain; Output feedback control; Actuator saturation; Parameter-dependent Lyapunov function; Stabilization; Saturation; Control program; Non linear control; Feedback regulation; Linear parameter varying system; Linear time; Scheduling; Restricted #2 gain; Attractor; Optimization; Closed feedback; Asymptotic stability; Discrete time; Open loop; Linear matrix inequality; Output feedback; Actuator; Lyapunov function; Quadratic function
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2007.12.011

In this paper, we present a new output feedback control approach for discrete-time linear systems subject to actuator saturations using parameter-dependent Lyapunov functions. The saturation level indicator serves as a scheduling parameter. The resulting nonlinear controller is expressed in a quasi-LPV (linear parameter-varying) form, and the stabilization and disturbance attenuation problems are formulated and solved as finite-dimensional linear matrix inequality (LMI) optimization problems. Our approach is less conservative than a single quadratic Lyapunov function method. Specifically, the proposed output feedback control law asymptotically stabilizes the open loop system with a larger domain of attraction and achieves better disturbance attenuation under energy and magnitude bounded disturbances.