The second type of method is based on the framework of Lyapunov-Krasovskii functional (LKF) and linear matrix inequality (LMI).
The problem of stability analysis by using the LKF and the LMI is that the criterion obtained has more or less conservatism.
This section derives delay-dependent stability criteria of GRN (2) by constructing the LKF with triple integral terms and applying the proposed WTDII (20) to estimate the double integral terms appearing in its derivative.
For GRN (2) with a delay satisfying (5), the following stability criterion is derived by using the proposed WTDII (27), together with Lemmas 1, 2, and 5, to estimate the derivative of the LKF
Calculating the derivative of the LKF along the solutions of GRN (11) yields
It is worth noticing that the construction of LKF can be improved by adding
In this paper, we have studied the stability for a class of neutral-type Lure systems with time-varying delays and sector bounded nonlinearities by using a new LKF. The LKF contains not only double-integral terms but also triple-integral terms.
It is significant to observe that LKF method deals with functionals which essentially have scalar values whereas Lyapunov-Razumikhin function (LRF) method involves only functions rather than functionals.
In some cases, the LKF involving terms depending on the state derivatives [[??].sub.t] are quite effective in the derivation of the stability conditions.
On choosing the LKF (31), a delay-independent stability condition can be derived in the following form.
Using the free-weighting , the following DDS condition can be derived based on the LKF (47).
Following, we proceed to study the DDS of system(54) using the following LKF candidate: