Abstract
This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results.
Highlights
Lur’e control system is an important nonlinear control system
In order to further reduce stability criterion’s conservatism, sector bounds and slope bounds are employed to a Lyapunov-Krasovskii functional through convex representation of the nonlinearities so that some new improved criteria were established by Lee and Park in [12] and Yin et al in [15], respectively
I is identity matrix; ∗ represents the elements below the main diagonal of a symmetric block matrix; real matrix P > 0(
Summary
Lur’e control system is an important nonlinear control system. Since the notion of absolute stability was first time introduced by Lur’e in [1], the problem of the absolute stability of Lur’e control system has been widely studied for several decades (see [2,3,4,5,6]). Because of the existence of time delays, stochastic disturbances, parameter uncertainties, and so on, the convergence of Lur’e system may often be destroyed. This makes the design or performance for the corresponding closed-loop systems become difficult. By employing linear matrix inequality and matrix decomposing technique, Cao and Zhong [6] researched the absolute stability problem of Lur’e control systems with multiple time delays and nonlinearities and established some improved delay-dependent criteria. In order to further reduce stability criterion’s conservatism, sector bounds and slope bounds are employed to a Lyapunov-Krasovskii functional through convex representation of the nonlinearities so that some new improved criteria were established by Lee and Park in [12] and Yin et al in [15], respectively. I is identity matrix; ∗ represents the elements below the main diagonal of a symmetric block matrix; real matrix P > 0(
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