New gain-scheduling control conditions for time-varying delayed LPV systems. Issue 2 (January 2022)

• Record Type: Journal Article
• Authors: de Souza, Lucas T.F.; Peixoto, Márcia L.C.; Palhares, Reinaldo M.
• Is Part Of: Journal of the Franklin Institute. Volume 359:Issue 2(2022)
• Page Start: 719
• Page End: 742
• Publication Date: 2022-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.04.029
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper investigates the problem of stability and state-feedback control design for linear parameter-varying systems with time-varying delays. The uncertain parameters are assumed to belong to a polytope with bounded known variation rates. The new conditions are based on the Lyapunov theory and are expressed through Linear Matrix Inequalities. An alternative parameter-dependent Lyapunov-Krasovskii functional is employed and its time-derivative is handled using recent integral inequalities for quadratic functions proposed in the literature. As main results, a novel sufficient stability condition for delay-dependent systems as well as a new sufficient condition to design gain-scheduled state-feedback controllers are stated. In the new proposed methodology, the Lyapunov matrices and the system matrices are put separated making it suitable for supporting in a new way the design of the stabilization controller. An example, based on a model of a real-world problem, is provided to illustrate the effectiveness of the proposed method.