Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

• Published in: International journal of robust and nonlinear control Vol. 31; no. 14; pp. 6585 - 6601
• Main Authors: Figueiredo, Larissa S., Lacerda, Márcio J., Leite, Valter J. S.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.09.2021
• Subjects: Actuators; Attraction; Control stability; Estimates; Feedback control; Initial conditions; Liapunov functions; LPV systems; Parameter estimation; polynomially dependent Lyapunov functions; Polynomials; rational controllers; saturating actuators; Stabilization; State feedback; Time varying control systems
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5625

This article investigates the local stabilization problem for the class of discrete‐time linear parameter varying (LPV) systems subject to saturating actuators. The main contributions are new convex conditions for synthesizing rational parameter‐dependent state feedback gain controllers, ensuring the local stability of the closed‐loop system for a set of initial conditions. We propose two design conditions for the local stabilization of the considered class of systems, which may lead to complementary results. We use a homogeneous polynomial parameter‐dependent (HPPD) based structure on the matrices variables. Thanks to a level set defined from an HPPD based Lyapunov function, we get less conservative estimates of the region of attraction. We provide a generalization of previous formulations from the literature to compute the intersection of parameter‐dependent ellipsoidal sets through finite‐dimensional conditions. The parameter‐dependent controller gains may assume rational structures on the time‐varying parameters, yielding better estimates of the region of attraction, as well as a broad set of stabilizable systems. Two examples illustrate the numerical aspects of the proposed conditions and give the reader a perspective of the relations concerning the conservatism and the degree of the HPPD functions.