Robust Delay-Dependent Stability Criteria for Time-Varying Delayed Lur’e Systems of Neutral Type

Abstract

This paper deals with the problem of the robust delay-dependent stability of uncertain Lur'e systems with neutral-type time-varying delays. By constructing a set of Lyapunov-Krasovskii functional, less conservative robust stability criteria are derived in terms of linear matrix inequalities. The contribution in reduced conservation of the proposed stability criteria relies on the reciprocally convex method and Wirtinger inequality, which provides tighter upper bound than Jensen inequality. Three numerical examples are provided to show the effectiveness of the proposed method.

Secondary delay‐partition approach on robust performance analysis for uncertain time‐varying Lurie nonlinear control system

“…In the recent, a number of remarkable results have been proposed on the stability analysis of delayed LCS . For instance, in Gao et al, by using Lyapunov‐Krasovskii functional (LKF) and free‐weighting matrix approach, new delay‐dependent synchronization criteria are obtained.…”

“…In another study, for the sake of reducing the conservatism of the stability criterion, the time derivative of the term in the LKF is tightly bounded by making use of slack matrices. In Liu et al, less conservative robust stability criteria are derived by using the reciprocally convex method and Wirtinger inequality. In other studies, when estimating the upper bound of the derivative of the LKF, the term was divided into and rather than directly estimation, which reduces considerable conservatism.…”

Novel delay-dependent robust stability criteria for neutral-type time-varying uncertain Lurie nonlinear control system with mixed time delays

“…The design of a PD controller for robust H ∞ stabilization of uncertain LCS with sector and slope restricted nonlinearities has been studied by using convex properties of the nonlinearities in [34]. By introducing an appropriate LKF and utilizing second order reciprocal convex combination technique, improved delay-dependent stability criteria have been derived in terms of LMIs in [15,24]. Paper in [19] has proposed a new method to study LCS with mixed time-varying delays.…”

Absolute stability of general neutral Lurie indirect control systems with unbounded coefficients

“…By introducing some triple-integral terms in LKF, Duan et al considered the stability problem of uncertain neutral-type Lur'e systems with time-varying delays in [17], and the derived criteria were less conservative than some proposed in [16,[18][19][20]. Additionally, robust absolute stability for uncertain Lurie interval time-varying delay systems of neutral type has been addressed and some stability results have been reported; see [21][22][23][24] and the references therein.…”

“…In [9,[16][17][19][20][21][22][23][24], they require the system coefficients to be uncertain but norm-bounded. Until now, most results concerning neutral Lurie systems required that the system coefficients be bounded.…”