Novel stability and stabilization conditions for time-delayed LPV systems: a linear matrix inequality-based approach

• Autor(a) principal: Lucas Tadeu Franco de Souza
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/34931
• topic: Linear parameter-varying (LPV) systems; Time-delay systems; Gain-scheduled control; Delay-dependent stability criterion; Engenharia elétrica; Desigualdades matriciais lineares; Liapunov, Funções de

This work investigates the problem of stability, state-feedback and static output-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 new sufficient conditions are stated to design gain-scheduling state-feedback and also gain-scheduling static output-feedback control. 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 controllers. Some examples, including some based on models of real-world problems, are provided to illustrate the effectiveness of the proposed methods.