Interval-like Time-varying Delay Research Articles

H_∞ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach

This paper addresses the problem of finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. Next, a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally, numerical examples are provided to illustrate the validity and applicability of the presented conditions.
 Keywords: Discrete-time neural networks, performance, finite-time stability, time-varying delay, linear matrix inequality.

Stability analysis of discrete-time neural networks with an interval-like time-varying delay

This paper studies the stability of discrete-time neural networks with an interval-like time-varying delay via the Lyapunov–Krasovskii (L–K) functional method. Firstly, a general free-matrix-based (GFMB) summation inequality is proposed, which includes the auxiliary-function-based and conventional free-matrix-based ones. Secondly, a novel L–K functional is deliberately constructed to make full advantage of the newly-developed GFMB summation inequality. Finally, a new stability condition is derived and two widely-used numerical examples are presented to show the effectiveness of the proposed approach.

On designing state estimators for discrete-time recurrent neural networks with interval-like time-varying delays

Abstract This paper deals with designing state estimators for a class of discrete-time recurrent neural networks with interval-like time-varying delays. Based on a delay bi-decomposition idea, a proper Lyapunov functional is introduced, which takes into account more information on the interval-like time-varying delay and the neuronal activation function. This Lyapunov functional, together with an improved reciprocally convex inequality, is employed to derive a sufficient condition to design suitable Luenberger-type estimators by solutions to linear matrix inequalities. An example is taken to show the effectiveness of the proposed method.

A Novel Finite-Sum Inequality-Based Method for Robust $H_\infty$ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

This paper is concerned with the problem of robust ${H}_{\infty}$ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust ${H}_{\infty}$ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay

This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.

Stability criterion for uncertain 2-$D$ discrete systems with interval-like time-varying delay employing quantization/overflow nonlinearities

This paper considers the problem of global asymptotic stability of a class of two-dimensional (2-$D$) uncertain discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under the influence of various combinations of quantization/overflow nonlinearities and interval-like time-varying delay in the state. The systems under consideration involve parameter uncertainties that are assumed to be deterministic and norm-bounded. A delay-dependent stability criterion is established by bounding the forward difference of the 2-$D$ Lyapunov functional using the reciprocally convex approach. The criterion is compared with a recently reported criterion.

A New Delay-Dependent Stability Criterion for Uncertain 2-D Discrete Systems Described by Roesser Model Under the Influence of Quantization/Overflow Nonlinearities

This paper considers the problem of global asymptotic stability of a class of two-dimensional uncertain discrete systems described by the Roesser model under the influence of various combinations of quantization/overflow nonlinearities and interval-like time-varying delay in the state. The systems under consideration involve parameter uncertainties that are assumed to be deterministic and norm-bounded. A delay-dependent stability criterion is derived by estimating the forward difference of the Lyapunov functional based on the reciprocally convex approach. Examples are provided to illustrate the effectiveness of the proposed criterion.

Stability Criteria for Uncertain Discrete-Time Systems under the Influence of Saturation Nonlinearities and Time-Varying Delay

The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.

Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay

This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results.

LMI-based criterion for robust stability of 2-D discrete systems with interval time-varying delays employing quantisation / overflow nonlinearities

This paper is concerned with the problem of global asymptotic stability of a class of nonlinear uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space model with time-varying state delays. The class of systems under investigation involves norm bounded parameter uncertainties, interval-like time-varying delays and various combinations of quantisation and overflow nonlinearities. A linear matrix inequality-based delay-dependent criterion for the global asymptotic stability of such systems is proposed. An example is given to illustrate the effectiveness of the proposed method.

A new admissibility condition of discrete-time singular systems with time-varying delays

This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.

Stability Analysis of Linear Discrete-Time Systems with Interval Delay: A Delay-Partitioning Approach

This paper considers the problem of asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By using a delay partitioning-based Lyapunov functional, a new criterion for the asymptotic stability of such systems is proposed in terms of linear matrix inequalities (LMIs). The proposed stability condition depends on both the size of delay and partition size. The presented approach is compared with previously reported approaches.

New Stability Criteria for Linear Discrete-Time Systems With Interval-Like Time-Varying Delays

This technical note is concerned with stability of linear discrete-time systems with interval-like time-varying delays. Two new stability criteria are derived by constructing a new Lyapunov functional and utilizing two novel techniques for estimating the forward difference of the Lyapunov functional. The relationship between these stability criteria and some existing ones is established. Through the relationship, it is clear that these stability criteria are less conservative than some existing ones, which is confirmed by a numerical example.

The Delay-Dependent for Discrete-Time Systems

Problem statement: This study is concerned with the problem of delay- dependent stability analysis for discrete-time systems with interval-li ke time-varying delays. Conclusion/Recommendations: The problem is solved by applying a novel Lyapunov functional and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. into account. It is worth noting that the closed-lo op system resulting from a delayed controller is actua lly a time-delay system. Therefore, stability results o f time-delay systems could be applied to design time- delayed controller. The present study a new Lyapunov functional, an improved delay-dependent stability criterion for discrete-time systems with time-varying delays is presented in terms of LMIs. It is shown that the obtained result is less conservative than those in. Example is providing, respectively, to demonstrate the reduced conservatism of the proposed stability crit erion and the effectiveness of the proposed design method . Preliminaries: Lemma 2.1 (Agarwal, 2000) the zero solution of difference system is asymptotic stabili ty if there exists a positive definite function n

Stability Criterion for Discrete-Time Systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.

Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H ∞ control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H ∞ performance is derived. Second, a memoryless H ∞ state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H ∞ performance of a system.

Improved Delay-Dependent $H_{\infty }$ Filtering Design for Discrete-Time Polytopic Linear Delay Systems

This brief revisits the problem of delay-dependent robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filtering design for discrete-time polytopic linear systems with interval-like time-varying delay. Under the condition whether the unknown parameters can be measured online or not, a parameter-dependent or a parameter-independent filter is respectively developed which guarantees the asymptotic stability of the resulting filtering error system with robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance gamma. It is shown that by using a new linearization technique incorporating a bounding technique, a unified framework can be developed such that the full-order and reduced-order, the parameter-dependent and parameter-independent filters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and merits of the proposed approach.