Research On The Stability And Control For Neutral-type Lur’e System

Delay phenomenon is often encountered in many practical systems, such as biological systems, chemical systems, electronic systems and network control systems. However, time-delay usually is the main cause of instability and bad performance. Therefore, in order to study the effects of delay on the system, the domestic and foreign experts and scholars have widely researched into time-delay systems. Furthermore, the neutral-type Lur’e system is a class of complicated time-delay and widely used systems. It is great theoretical significance and practical values to study this system.This paper mainly studies the delay-dependent stability and the robust stability of the neutral-type Lur’e system with time-varying delay, and the synchronization controller design problem.First, starting from the research tools, a class of Jensen inequality is improved based on the Fourier theory, function-construction methods and integral operation skill. And it has been generalized to conservative lower double integral inequality.The rationality, feasibility and superiority of the inequalities have been justified.Then, this paper considers the delay-dependent stability analysis of neutral-type Lur’e systems with time-varying delays.Based on the delay-partitioning, this paper constructs efficiently a new class of Lyapunov-Krasovskii functional, and gets he new less conservative robust stability criteria.Finally, this paper based on the study of stability criteria for Lur’e system, we analysis the synchronization controller for this system. Combined with the new inequality and reciprocal convex approach, we get some lower conservative synchronization controller.