50 research outputs found
An improved delay-dependent stabilization criterion of linear time-varying delay systems: An iterative method
summary:This paper presents delay-dependent stabilization criteria for linear time-varying delay systems. A less conservative stabilization criterion is derived by invoking a new Lyapunov-Krasovskii functional and then, extended reciprocally convex inequality in combination with Wirtinger's inequality is exploited to obtain an improved stabilization criterion where a set of nonlinear matrix inequalities is solved by applying the cone complementarity algorithm. The proposed stabilization technique transforms a non-convex problem into a nonlinear trace minimization problem which is solved by an iterative approach. Numerical examples are considered to demonstrate the effectiveness of the proposed stabilization criteria and the presented iterative algorithm outperforms some existing results
New summation inequalities and their applications to discrete-time delay systems
This paper provides new summation inequalities in both single and double
forms to be used in stability analysis of discrete-time systems with
time-varying delays. The potential capability of the newly derived inequalities
is demonstrated by establishing less conservative stability conditions for a
class of linear discrete-time systems with an interval time-varying delay in
the framework of linear matrix inequalities. The effectiveness and least
conservativeness of the derived stability conditions are shown by academic and
practical examples.Comment: 15 pages, 01 figur
STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS
In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology
Delay-dependent criterion for exponential stability analysis of neural networks with time-varying delays
This note investigates the problem of exponential stability of neural networks with time-varying delays. To derive a less conservative stability condition, a novel augmented Lyapunov-Krasovskii functional (LKF) which includes triple and quadruple-integral terms is employed. In order to reduce the complexity of the stability test, the convex combination method is utilized to derive an improved delay dependent stability criterion in the form of linear matrix inequalities (LMIs). The superiority of the proposed approach is demonstrated by two comparative examples
Dissipative Stabilization of Linear Systems with Time-Varying General Distributed Delays (Complete Version)
New methods are developed for the stabilization of a linear system with
general time-varying distributed delays existing at the system's states, inputs
and outputs. In contrast to most existing literature where the function of
time-varying delay is continuous and bounded, we assume it to be bounded and
measurable. Furthermore, the distributed delay kernels can be any
square-integrable function over a bounded interval, where the kernels are
handled directly by using a decomposition scenario without using
approximations. By constructing a Krasovski\u{i} functional via the application
of a novel integral inequality, sufficient conditions for the existence of a
dissipative state feedback controller are derived in terms of matrix
inequalities without utilizing the existing reciprocally convex combination
lemmas. The proposed synthesis (stability) conditions, which take dissipativity
into account, can be either solved directly by a standard numerical solver of
semidefinite programming if they are convex, or reshaped into linear matrix
inequalities, or solved via a proposed iterative algorithm. To the best of our
knowledge, no existing methods can handle the synthesis problem investigated in
this paper. Finally, numerical examples are presented to demonstrate the
effectiveness of the proposed methodologies.Comment: Accepted by Automatic
New delay-dependent stability criteria for recurrent neural networks with time-varying delays
Dimirovski, Georgi M. (Dogus Author)This work is concerned with the delay-dependentstability problem for recurrent neural networks with time-varying delays. A new improved delay-dependent stability criterion expressed in terms of linear matrix inequalities is derived by constructing a dedicated Lyapunov-Krasovskii functional via utilizing Wirtinger inequality and convex combination approach. Moreover, a further improved delay-dependent stability criterion is established by means of a new partitioning method for bounding conditions on the activation function and certain new activation function conditions presented. Finally, the application of these novel results to an illustrative example from the literature has been investigated and their effectiveness is shown via comparison with the existing recent ones
On Less Conservative Stability Criteria for Neural Networks with Time-Varying Delays Utilizing Wirtinger-Based Integral Inequality
This paper investigates the problem of stability analysis for neural networks with time-varying delays. By utilizing the Wirtinger-based integral inequality and constructing a suitable augmented Lyapunov-Krasovskii functional, two less conservative delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). Three numerical examples are included to explain the superiority of the proposed methods by comparing maximum delay bounds with the recent results published in other literature