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Improved delay-dependent stability criteria for uncertain Lur’e systems with sector and slope restricted nonlinearities and time-varying delays. (English) Zbl 1172.34047
The paper investigates the absolute stability of uncertain time delay Lur’e systems that have time-varying delays and sector and slope restricted nonlinearities. In the mathematical model of this kind of Lur’e systems, it is assumed that the nonlinear function and the derivatives of the nonlinear function are bounded, respectively, the time-varying delays are bounded and the derivatives of the time-varying delays are less than one. By constructing Lyapunov-Krasovskii functionals, a new criterion for absolute stability of the Lur’e systems is presented in terms of linear matrix inequality (LMI). This criterion is dependent on the size of the time delays and the derivative of the time-varying delays, which is usually less conservative than delay-independent ones.
##### MSC:
 34K20 Stability theory of functional-differential equations 34K99 Functional-differential equations
##### Keywords:
Lur’e systems; time-varying delay; stability; LMIs