Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

Absolute-in-Nonlinearity-and-Delay Stability in Quadratic Mean of Stochastic Differential-Difference Systems with Poisson Switchings

Algebraic coefficient conditions of absolute asymptotic stability in quadratic mean of the equilibrium of a stochastic dynamic automatic control system are obtained in the present paper. A mathematical model of this system is a system of Ito-Skorokhod stochastic differential-difference delay equations with several standard Wiener processes, Poisson perturbations, and a finite number of delays.     

Robustness of exponential stability to singular perturbations and delays

Singularly perturbed nonlinear differential equations with small time delays in the slow variables are considered. Averages of the fast variables are used in order to obtain a sufficient condition under which the exponential stability of the slow subsystem is robust to singular perturbations and delays.     

Control of time delay processes with uncertain delays: Time delay stability margins

In this paper, the stability of time delay processes that have uncertain delays is considered, and the maximum allowable perturbation which may occur in the time delays so as to maintain stability are determined. In particular, the characteristic equations of time delay systems are quasipolynomials, whose roots determine the stability of such systems, and the root-locus of these equations in specified desired regions is investigated. A numerical algorithm is presented for the calculation of the time delay stability margins in the space of time delays for such systems, and the size of the stability hyperspheres in this space is computed. To illustrate the procedure, the algorithm is applied to process control systems with uncertain delays and the allowable perturbations in the time delays of these systems are then computed.     

带非线性扰动的不确定多时变时滞系统H∞鲁棒稳定性

研究了带非线性扰动的不确定多时变时滞系统的H∞鲁棒稳定性．其中不确定项是范数有界的,非线性扰动满足线性约束．基于Lyapunov-Krasovskii泛函,根据矩阵不等式技术和非线性处理方法,提出了两个新的时滞稳定性的结果．最后给出了两个示例,表明本文提出的方法与存在的文献结果相比,具有较少的保守性和良好的有效性．     

Stability and robustness analysis for human pointing motions with acceleration under feedback delays

Pointer acceleration is often used in computer mice and other interfaces to increase the range and speed of pointing motions without sacrificing precision during slow movements. However, the effects of pointer acceleration are not yet well understood. We use a system perspective and feedback control to analyze the effects of pointer acceleration. We use a new pointer acceleration model connected in feedback with the vector integration to endpoint model for pointing motions. When there are no feedback delays, we prove global asymptotic stability of the closed loop system for a general class of acceleration profiles. We also prove robustness under delays and perturbations by building Lyapunov–Krasovskii functionals for delay systems, and we find state performance bounds using robust forward invariance with maximal perturbation sets. The results are relevant to designing pointing interfaces, and our simulations illustrate the good performance of our control under realistic operating conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solutions for recurrent neural networks with impulsive perturbations and delays. Further, by using numerical simulation method, the influences of the impulsive perturbations on the inherent oscillations are investigated.     

A new result on stability analysis for stochastic neutral systems

This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results.     

Delay-dependent robust stability of linear systems with non-commensurate time varying delays

In this article we investigate the robust stability of uncertain systems with non-commensurate time varying delays. Two types of perturbations are considered. First, we consider time varying and unknown but norm bounded uncertainties. Next systems with polytopic-type uncertainties are studied. Based on Finsler's lemma we propose a new method for achieving less restrictive sufficient conditions for delay-dependent robust stability. The results are presented in terms of linear matrix inequalities. Three examples are given for illustration and comparison with previous results.     

Stability and robust stability of positive Volterra systems

We study positive linear Volterra integro‐differential systems with infinitely many delays. Positivity is characterized in terms of the system entries. A generalized version of the Perron–Frobenius theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L¹‐stability and exponential asymptotic stability. Also, the concept of stability radii, determining the maximal robustness with respect to additive perturbations to L¹‐stable system, is introduced and it is shown that the complex, real and positive stability radii coincide and can be computed by an explicit formula. Copyright © 2011 John Wiley & Sons, Ltd.     

Exponential stability of slowly varying discrete systems with multiple state delays

We give sufficient conditions for the exponential stability of a class of perturbed time‐varying difference equations with multiple delays and slowly varying coefficients. Under appropriate growth conditions on the perturbations, combined with the ‘freezing’ technique, we establish explicit conditions for global exponential stability. Copyright © 2012 John Wiley & Sons, Ltd.     

A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays

Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditions that guarantee stability of the network under consideration. Lyapunov–Razumikhin functions and the local small gain condition are utilised to obtain such conditions. Our stability conditions for the logistics network are based on the information about the interconnection properties between logistic locations and their production rates. Finally, numerical results are provided to demonstrate the proposed approach.     

Robust stability of delay difference systems under fractional perturbations in infinite-dimensional spaces

In this article we study the robust stability of difference systems with delays under fractional perturbations in infinite-dimensional spaces. First, the estimates of the complex stability radius are addressed. Second, it is shown that for positive linear systems, the complex, real and positive stability radii coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results.     

Stability impact of small delays in proportional–derivative state feedback

This paper points out specific stability problems of the state derivative and proportional–derivative state feedback which may result from the presence of otherwise negligible delays in the control loops. It is shown that the stability problems arise from the neutral character of the closed-loop system with the state derivative action under small delay perturbations. As the main result, a stability criterion is derived for a safe implementation of the state derivative feedback. Furthermore, a scheme including filtered state derivative feedback is proposed to overcome the destabilizing effects of small feedback delays. Two application examples are presented. From a theoretical point of view, the main contribution of the paper lies in the stability theory of linear neutral equations with dependent delays, subjected to delay perturbations.     

On loop phase margins of multivariable control systems

This paper has two contributions. One is introduction of loop phase margins for multivariable control systems, which extends the concept of phase margin in SISO systems to MIMO systems. The other one is development of an algorithm for computing the loop phase margins. The algorithm is composed of two steps. The first is to find the stabilizing ranges of loop time delay perturbations of the MIMO system using an LMI-based stability criterion derived here. The second is to convert these stabilizing ranges of loop time delays into the stabilizing ranges of loop phases. Two numerical examples are given to illustrate the effectiveness of the proposed approach.     

多时滞Hopfield神经网络的鲁棒稳定性分析及吸引域的估计

The robust stability of a class of Hopfield neural networks with multiple delays and parameter perturbations is analyzed. The sufficient conditions for the global robust stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. The conditions take the form of linear matrix inequality (LMI), so they are computable and verifiable efficiently. Furthermore, all the results are obtained without assuming the differentiability and monotonicity of activation functions. From the viewpoint of system analysis, our results provide sufficient conditions for the global robust stability in a manner that they specify the size of perturbation that Hopfield neural networks can endure when the structure of the network is given. On the other hand, from the viewpoint of system synthesis, our results can answer how to choose the parameters of neural networks to endure a given perturbation.     

Robust stabilizers for an implicit dynamical delay system of the neutral type

A feedback stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed delays. The imperfections acting on the systems, which may be time‐, state‐, delayed state‐, and/or input‐dependent, are modelled as additive nonlinear perturbations influencing a known set of nonlinear functional differential equations of the neutral type. Sufficient conditions, which include a delay‐dependent matrix inequality and a delay‐dependent stability criterion involving some bounding parameters for the uncertainty in the system, are presented and a class of robust feedback stabilizers, including both memoryless and those with memory, are designed to guarantee a prescribed stability property for the class of implicit systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Improved exponential stability criteria for uncertain neutral system with nonlinear parameter perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.     

Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.     

具有非线性扰动和混合时滞的中立型系统的时滞依赖鲁棒稳定性

This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discrete-delay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.