Lurie Uncertain Time-delay Systems Robust Stability Study

Lurie system is a kind of typical nonlinear systems. It has been widespread concerned by researchers since which was been first proposed in1940s. Many new results which are about absolute stability of Lurie systems have been found. Delays and uncertainties can make the system unstable or unable to achieve a specific function, therefore, the research of systems which contain delays and uncertainties has important significance in stability study.In this thesis, the stability for a class of Lurie systems and the robust stability for a class of uncertain Lurie systems are studied. Lurie systems include a nonlinear feedback term and output items correlated with the delay term. The purpose of this paper is to find an improved stability criterion for such a system and to reduce the conservatism of the results. Based on augmented Lyapunov-Krasovskii functions, combined with time delay decomposition method, Jensen inequality method and reciprocally convex approach, a new stability criterion is obtained, and numerical examples are given to demonstrate the superiority and effectiveness of the results. The main contents are as follows:For a class of Lurie systems with varying delay, by constructing a new type of augmented Lyapunov-Krasovskii functional combined with the reciprocally convex approach, a new delay-dependent stability criterion is proposed in terms of linear matrix inequalities. Numerical examples show that our method can lead to upper allowable delay bounds which are better than other methods in the literature. This verifies the effectiveness and advantage of the present results.For the norm bounded uncertain Lurie systems, by extending the approach for nominal systems, a new robust stability condition is obtained. Numerical examples show the superiority and effectiveness of the results.