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Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions
Author(s) -
Figueiredo Larissa S.,
Lacerda Márcio J.,
Leite Valter J. S.
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5625
Subject(s) - mathematics , lyapunov function , homogeneous polynomial , control theory (sociology) , polynomial , generalization , intersection (aeronautics) , function (biology) , state (computer science) , nonlinear system , computer science , control (management) , mathematical analysis , physics , matrix polynomial , quantum mechanics , artificial intelligence , evolutionary biology , engineering , biology , aerospace engineering , algorithm
Abstract 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.