Novel tests for stability analysis of time-delayed systems: a linear matrix inequality-based approach

• Autor(a) principal: Fúlvia Stefany Silva de Oliveira
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/34493
• topic: Time-delay systems; Stability analysis; Linear matrix inequalities; LyapunovKrasovskii theory; Kalman-Yakubovich-Popov lemma; Engenharia elétrica; Desigualdades matriciais lineares; Kalman-Yakubovich-Popov, Lema de

Stability analysis of time-delayed systems has been a very active research field in control theory over the last decades. The interest relies on the fact that the time-delay is an inherent phenomenon of a broad class of systems in different fields, like engineering, biology, and economics. Moreover, time-delay systems belong to the class of infinite-dimensional differential equations, making their stability analysis a very complex problem. Although the improvements over the last years, the existing methods to deal with this problem still have limitations. In this thesis, improved methods are proposed to assess the stability of linear time-invariant (LTI) systems with constant and time-varying delay. A first contribution is an alternative method to check exactly the (strong) delay-independent stability of systems with constant time-delay. The proposed approach is to use a frequency-dependent Lyapunov stability inequality, with matrices of polynomial type, to indirectly determine the existence of crossing roots on the imaginary axis. The resulting stability criterion is formulated as a linear matrix inequality condition using the Kalman-Yakubovich-Popov (KYP) lemma. As a second contribution, new sufficient conditions are proposed for delay-dependent stability of systems with time-varying delay based on a new augmented affine parameter-dependent Lyapunov-Krasovskii functional (LKF). This stability criterion is specified as a negativity condition for a quadratic function parameterized by the delay. It is also presented a method to translate such a condition into a finite-dimensional convex optimization problem that can be checked exactly in terms of LMI conditions. Finally, the delay-dependent stability conditions are extended to the case of systems with multiple time-varying delays. Numerical examples taken from the literature show that the proposed methods can improve the related existing results.