New gain-scheduling control conditions for time-varying delayed LPV systems |
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| Institution: | 1. Federal University of Minas Gerais, Graduate Program in Electrical Engineering, Brazil;2. Federal University of Minas Gerais, Department of Electronics Engineering, Brazil;1. Universidad de Monterrey, Av. I. Morones Prieto 4500 Pte., 66238, San Pedro Garza García N.L., México;2. Universidad Autónoma de Nuevo León, Av. Universidad s/n, 66450, San Nicolás de los Garza N.L., México;3. Université Grenoble Alpes, GIPSA-lab, F-3800 Grenoble, France;1. Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6G 2W3, Canada;2. Department of Electrical Engineering, Sahand University of Technology, Tabriz, Iran;1. Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, 61 Bolshoy Prospekt V.O., St. Petersburg 199178, Russia;2. Gubkin University, 65 Leninsky Prospekt, Moscow 119991, Russia;1. Department of Electrical Engineering, University of Technology of Paraná – UTFPR Cornélio Procópio 86300-000, PR, Brazil;2. Federal Institute of São Paulo – IFSP, Campus Avaré, Avaré 18707-150, SP, Brazil |
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| 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. |
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