Stability Criteria For Systems Research Articles

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

This paper is concerned with exponential stability analysis for linear continuous positive systems with bounded time-varying delay. Our approach is based on Lyapunov---Krasovskii functional with delay decomposition. The main idea is to divide uniformly the discrete delay interval into multiple segments and then to choose proper functionals with different weighted matrices corresponding to different segments. The synthesis of our delay-dependent sufficient stability criteria is formulated in terms of linear matrix inequalities. The proposed results are shown to be less conservative compared to other results from the literature. Some illustrative examples are given to show the effectiveness of the obtained results.

An enhanced stability criterion for time-delay systems via a new bounding technique

In the past few years, a great deal of effort has been devoted to improve delay-dependent conditions for stability of linear systems with an interval time-varying delay. To reduce conservatism of stability conditions, in the framework of the Lyapunov–Krasovskii functional (LKF) method, the bounding technique plays a key role. In this paper, a new bounding technique based on a new integral inequality is proposed. By employing the newly bounding technique proposed in this paper, an enhanced stability criterion for a class of linear systems with an interval time-varying delay is derived. The effectiveness and a significant improvement of the obtained results are shown by numerical examples.

Generalized Lag Anti-Synchronization of Coupled Chaotic Systems

This paper aims to study the generalized lag anti-synchronization of two dynamical systems via linear transformation. The method is based on the stability criterion of linear systems and the lag anti-synchronization of driving and response systems are ensured by that all roots of characteristic equations of the jacobian matrix have negative real parts. The linear generalized lag anti-synchronization can be robustly achieved, without calculating the Lyapunov exponents. In the proposed method the functional relation between driving system and response system are also achieved.

Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

This study investigates the robust stability of fractional-order systems with interval coefficients and a time-delay. By the Minkowski Sum, the vertices of value set with respect to the characteristic function of the investigated fractional-order system are offered, avoiding the calculations of the redundant vertices. Meanwhile, a function depending on the obtained vertices is defined to represent the position relationship between the origin and the value set. Based on the zero exclusion principle, we propose sufficient and necessary conditions to determine the robust stability of fractional-order systems with interval uncertain coefficients and a time-delay. Finally, illustrative examples are offered to verify the effectiveness of the proposed robust stability criterion.

A further note on stability criteria for uncertain neutral systems with mixed delays

This paper is a further note on stability criteria for uncertain neutral systems with mixed delays. We firstly employed a new method to estimate the upper bound of the derivative of functional, and novel stability criteria are presented for nominal neutral system, which will obtain less conservatism. Then, several sufficient stability conditions are proposed for neutral systems with polytopic uncertainty and linear fractional norm-bound uncertainty. Lastly, three numerical examples are given to demonstrate the effectiveness and merit of the proposed results. In Appendix, the stability criteria in Lu et al. [21] are rectified.

Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems

This paper is concerned with stability of linear discrete time-delay systems. Note that a tighter estimation on a finite-sum term appearing in the forward difference of some Lyapunov functional leads to a less conservative delay-dependent stability criterion. By using Abel lemma, a novel finite-sum inequality is established, which can provide a tighter estimation than the ones in the literature for the finite-sum term. Applying this Abel lemma-based finite-sum inequality, a stability criterion for linear discrete time-delay systems is derived. It is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a Jensen-type inequality approach and a free-weighting matrix approach.

Further results on stability analysis of discrete-time systems with time-varying delays via the use of novel convex combination coefficients

This paper focuses on deriving an improved stability criterion for discrete time-delay systems via a Lyapunov–Krasovskii functional approach that takes advantage of triple summation terms. To this end, novel convex combination coefficients coupled with second-order time-varying delay terms are introduced, and the corresponding reciprocally convex approach is established with the use of the minimal number of slack matrix variables. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed method, with particular regard to robustness and H∞ performance.

Stability analysis for delayed high-order type of Hopfield neural networks with impulses

This paper can be regarded as the continuation of the work of the authors contained in papers (2015). At the same time, it represents the extension of the papers Lou and Cui (2007, [24]), Sannay (2007, [34]) and Acka et al. (2004, [1]). This work discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. By utilizing Lyapunov functional method and the linear inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. The exponential convergence rate of the equilibrium point is also estimated. Finally, we analyze and interpret four numerical examples proving the efficiency of our theoretical results and showing that impulse can be used to stabilize and exponentially stabilize some high-order Hopfield-type neural networks.

Stability analysis for discrete-time neural networks with time-varying delays and stochastic parameter uncertainties

This paper proposes new delay-dependent stability criteria for discrete-time neural networks with interval time-varying delays and probabilistic occurring parameter uncertainties. It is assumed that parameter uncertainties are changed with the environment, explored using random situations, and its stochastic information is included in the proposed method. By constructing a suitable Lyapunov–Krasovskii functional, new delay-dependent stability criteria for the concerned systems are established in terms of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Stability Criteria of Random Nonlinear Systems and Their Applications

Stochastic differential equations (SDEs) are widely adopted to describe systems with stochastic disturbances, while they are not necessarily the best models in some specific situations. This paper considers the nonlinear systems described by random differential equations (RDEs). The notions and the corresponding criteria of noise-to-state stability, asymptotic gain and asymptotic stability are proposed, in the m-th moment or in probability. Several estimation methods of stochastic processes are presented to explain the reasonability of the assumptions used in theorems. As applications of stability criteria, some examples about stabilization, regulation and tracking are considered, respectively. A theoretical framework on stability of RDEs is finally constructed, which is distinguished from the existing framework of SDEs.

Stability of time-delay systems via Wirtinger-based double integral inequality

Based on the Wirtinger-based integral inequality, a double integral form of the Wirtinger-based integral inequality (hereafter called as Wirtinger-based double integral inequality) is introduced in this paper. To show the effectiveness of the proposed inequality, two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities (LMIs). The advantage of employing the proposed inequalities is illustrated via two numerical examples.

Analysis and synthesis of fractional order repetitive control for power converters

Repetitive control is widely employed in power converters due to its zero-error compensation of periodic signals. However, conventional repetitive control is sensitive to frequency variations of the periodic signals. For example, in grid-connected applications, conventional repetitive controlled power converters will produce higher harmonics distortion under grid frequency variations. Based on finite impulse response (FIR) fractional delay filters, fractional order repetitive control (FORC) scheme provides fast on-line computation and frequency adaptability to compensate for harmonics in grid-connected applications at fixed sampling time. In this paper the analysis and synthesis of the proposed FORC are comprehensively investigated. A stability criterion for FORC systems is derived. As a case study, experimental tests on a standalone single-phase PWM inverter, supplying a non-linear rectifier load, are provided to evaluate the effectiveness of the proposed FORC.

Improved Stabilization for Continuous Dynamical Systems with Two Additive Time‐Varying Delays

AbstractThis paper studies the problem of stabilization criteria for systems with two additive time‐varying delays. First, the delay‐dependent stability condition for the systems is established through computing the more general Lyapunov functional. The Lyapunov functional is constructed by making full use of the property and the information of the systems, and the condition has advantages over the existing ones in the skillful combination of the delay decomposition and the reciprocal convex approach. Second, considered to be more flexible for the controller design with the introduced positive scalar, a new controller method is presented. Finally, two examples are provided to demonstrate the advantage of the results in this paper.

Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems

In this paper, we establish finite time stability (FTS) criteria for the nonlinear impulsive systems. By using a new concept called average impulse interval (AII), less conservative conditions are obtained for the FTS problem on the impulsive systems. Then we consider the linear time-invariant sampled-data systems by modeling such systems as linear impulsive systems. It is proved that when the AII of a sequence of impulsive signals ζ is equal to τα, the upper bound of the impulsive intervals could be very large, while the lower bound of the impulsive intervals could be also small enough. The obtained results are less conservative than the ones in the literature obtained for variable sampling intervals.

Improved integral inequality approach on stabilization for continuous-time systems with time-varying input delay

This study is concerned with the issue of output delay-dependent stabilization criteria for continuous-time systems with time-varying input delays. By introducing an augment Lyapunov–Krasovskii functional and a new integral inequality, a new reduced conservative condition is obtained in terms of linear matrix inequalities (LMIs). At last, numerical examples are also designated to demonstrate the effectiveness and reduced conservatism of the developed results.

Novel Criteria for Exponential Stability of Nonlinear Differential Systems With Delay

General nonlinear differential systems with time-varying delay are considered. Several explicit criteria for global exponential stability are presented. Two examples are given to illustrate the obtained results.

Linear stability of one‐dimensional non‐Darcy flow in broken rocks

SUMMARYConsidering the effect of non‐Darcy flow, the perturbation theory and normal mode method are introduced to analyze the linear stability of one‐dimensional non‐Darcy flow of gases in broken rocks. A stability criterion for linear systems is obtained theoretically when the steady states of pressure and velocity fields are perturbed, and the effects of the physical parameters on the linear governing system are studied theoretically and numerically. It is pointed out that the deviation coefficient from Darcy's law plays an important role in the governing system; the increasing absolute value of deviation coefficient from Darcy's law stabilizes the system, and the numerical results are shown graphically. Copyright © 2015 John Wiley & Sons, Ltd.

進行波圧力成分に関するシステム表現に基づく定在波型／進行波型熱音響システムに対する統一的な自励発振条件の解析

This paper presents a unied stability analysis method for thermoacoustic systems based on the Nyquist stability criterion for MIMO systems. The method consists of two procedures: (i) conventional frequency response function (transfer matrix) is transformed into the one for causal system whose input and output signals are incoming and outgoing traveling-wave pressure components; (ii) the transformed response is used to analyze the closed-loop stability by the Nyquist stability criterion for MIMO systems. It is shown that the stability analysis for both standing- and traveling-wave thermoacoustic engines can be carried out by a unied procedure. The analysis results are consistent with the actual situations of oscillation indicating reasonable stability and/or instability margins for various geometrical changes as well as the temperature ratios in engines.

On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach

In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1)=A0(k)+A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.

Maximum Lyapunov exponents and stability criteria of linear systems with variable delay

The Myshkis problem of the maximum Lyapunov exponent of a first-order linear differential equation with an arbitrary bounded delay is solved. The result obtained is generalized to a system of equations of arbitrary order, whose matrix has real eigenvalues. A sufficient condition for exponential stability is obtained for a system with complex eigenvalues.