Moreover, by applying the Lyapunov function method, a sufficient condition of couple-group consensus is established in terms of a matrix inequality when the communication topology is switching.
By using the Lyapunov method, a sufficient condition which guarantees that the filtering error system is stochastically stable and satisfies the passive performance is established.
Based on the Lyapunov stability theory and some stochastic system analysis method, a sufficient condition is obtained such that the closed-loop system is asymptotically stable in the mean-square sense and achieves a prescribed H∞ performance level.
(2) using the average dwell time method, a sufficient condition ensuring the exponential stability is obtained, meanwhile, the minimum running time of each subsystem, i.e., the running time of each phase can be calculated.
Combining the Lyapunov-like function method and the average dwell time method, a sufficient condition is derived for the switched polytopic system with asynchronous switching and data dropout to be globally, uniformly and asymptotically stable in terms of linear matrix inequality.
Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented system is stochastically stable and achieves an average H∞ performance level γ; the design procedure of the optimal distributed filter is also provided.
In this subsection, based on the Lyapunov method, a sufficient criterion of exponential outer synchronization which is easily verifiable is established in the form of coefficients.
By using the Lyapunov stability theory and the adaptive control method, a sufficient projective synchronization criterion for this neutral-type neural network model is derived.
El-Sayed [16] presented two iterative methods for calculating the positive definite solutions of the matrix equation (X-A^X^{-n}A=Q), for the integer (ngeq1), the first method is derived for a normal matrix A and for the second method a sufficient condition for convergence is given for (n = 2^{k}).
With this method, a sufficient number of slices and explants can be obtained from minimal amounts of tissue, enabling the study of several compounds within a single tumor specimen.
