Research on delay-independent stability for discrete-time interval systems with time-varying delay

This paper investigates the guaranteed cost control problem of uncertain non-linear systems with time-varying delays via the Takagi–Sugeno fuzzy model approach. Based on the Lyapunov–Krasovskii functional theory and the linear matrix inequality technique, a state feedback controller is proposed to stabilise the non-linear systems and minimise the guaranteed cost of the closed-loop systems. Both delay-dependent and delay-independent stability criteria are derived to guarantee the asymptotic stability of closed-loop systems. Furthermore, the supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the validity of the results developed in this paper.

This paper presents necessary and sufficient conditions for the quadratic stability and stabilization of dynamic discrete-time interval systems. The results are obtained in terms of linear matrix inequality (LMI). With the powerful LMI toolbox, it is very convenient to solve these problems. The illustrative examples show that this method is effective to check the robust stability and to design the stabilizing controller for dynamic discrete-time interval systems.

This paper treats the stability bound problem of discrete linear singularly perturbed system (SPSs) with time delay is treated. Using an appropriate Lyapunov-Krasovskii functional, satisfactory conditions formulated in terme of Linear Matrix Inequalities (LMIs) are proposed to analyse the asymptotic stability of SPSs. Delay independent and delay dependent stability criterion are treated. Illustrative examples are provided to demonstrate the efficiency of the proposed method.

Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

The problem of stabilization for time-delay systems with time-varying parametric perturbations is considered in this paper. Two delay-independent stability criteria and a family of memoryless state feedback controllers are proposed. The main feature of the present result is that both the criteria and the controllers do not involve any Riccati equations and are easy to he tested and be implemented. A numerical example is given to demonstrate the effectiveness of the present schemes.

This study presents novel sufficient conditions for both finite-time and practical stability of the continuous linear control systems with latency in the state variables. The analyzed systems are mathematically represented using the state space differential equations with time delay. The new delay-independent finite time stability criteria were generated utilizing the Lyapunov-Krasovskii functional. This functional is not required to have non-negative definite properties on the entire state space. Furthermore, it is not required that the derivations of the functional are negative along the trajectories as it is the case for conventional stability conditions. Consequently, the presented conditions can be implemented in a practical calculation without difficulties.

Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional

<abstract><p>Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results.</p></abstract>

This article concerns the stability and stabilisation of a linear system with both state and input delays. First, the combination of an augmented Lyapunov functional and the free-weighting-matrix technique yields a new delay-independent stability criterion that includes the widely used one as a special case. This criterion is then extended to a new delay-dependent stability criterion by employing an integral inequality. Based on that, a stabilisation approach to design a state feedback controller is presented that requires no parameter tuning, as is needed with some existing methods. Finally, numerical examples illustrate that the method is effective and is an improvement over existing ones.

In this note, we deal with the stability and stabilization problems for nonlinear quadratic discrete-time periodic systems. By using the quadratic Lyapunov function, and a so called periodic invariant set, delay-independent sufficient conditions for local stability and local stabilization for nonlinear quadratic discrete-time periodic systems are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

Delay-dependent H∞ control stabilization of linear systems with time-varying delays

This paper deals with the problem of robust stability of uncertain singular continuous systems with time-varying delays. The parametric uncertainties are assumed to be norm bounded. Delay dependent conditions are given to ensure that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are given in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method, and to compare with previous works.

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones.

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.

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.