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In this paper, we present a geometric method for describing the effects of the ‘delay-induced uncertainty’ on the stability of a standard Smith predictor control scheme. The method consists of deriving the ‘stability crossing curves’ in the parameter space defined by the ‘nominal delay’ and ‘delay uncertainty’, respectively. More precisely, we start by computing the ‘crossing set’, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their ‘complete classification’, including also the explicit characterization of the ‘directions’ in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included. [ABSTRACT FROM PUBLISHER]

This paper characterizes the stability crossing curves of a class of linear systems with gamma-distributed delay with a gap. First, we describe the crossing set, i.e., the set of frequencies where the characteristic roots may cross the imaginary axis as the parameters change. Then, we describe the corresponding stability crossing curves, i.e., the set of parameters such that there is at least one pair of characteristic roots on the imaginary axis. Such stability crossing curves divide the parameter space ℝ+2 defined by the mean delay and the gap into different regions. Within each such region, the number of characteristic roots on the right half complex plane is fixed. This naturally describes the regions of parameters where the system is stable. The classification of the stability crossing curves is also discussed. Some illustrative examples (Cushing equation in biology, traffic flow models in transportation systems, and control over networks of a simplified helicopter model) are also presented. [ABSTRACT FROM AUTHOR]

This note focuses on the stability analysis of some classes of nonlinear time-delay models, encountered as fluid models for TCP/AQM network. By combining analytical and numerical tools, the attractors of these models, as well as the local and global behaviors of the solutions are studied. Among others, the presence of a chaotic attractor is shown, which supports the proposition that TCP itself as a deterministic process can cause or contribute to chaotic behavior in a network. The main goals of the paper are firstly to provide qualitative and quantitative information on the dynamics of the models under consideration, and secondly to illustrate the capabilities of computational tools for stability and bifurcation analysis of delay differential equations to analyze fluid flow models. [ABSTRACT FROM AUTHOR]

Provides an overview of the stability and control of time-delay systems. Examples of time-delay systems; Stability criteria and performance measure; Feedback control.

The stability problem for systems with distributed delay is considered using discretized Lyapunov functional. The coefficients associated with the distributed delay are assumed to be piecewise constant, and the discretization mesh may be non-uniform. The resulting stability criteria are written in the form of linear matrix inequality. Numerical examples are also provided to illustrate the effectiveness of the method. The basic idea can be extended to a more general setting with more involved formulation. [ABSTRACT FROM AUTHOR]

Abstract: The structure of positive polynomials on a torus is derived from recent results of real algebraic geometry. As an application, we propose some simple conditions for testing the hyperbolicity/stability of a generic class of linear systems of retarded type. [Copyright &y& Elsevier]

Abstract: Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made up of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has also been shown that the TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyse the robust stability of the closed-loop system in the face of delay uncertainties that are present in data networks due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty. [Copyright &y& Elsevier]

Abstract: In this paper, a PD controller design for haptic systems under delayed feedback is considered. More precisely, a complete stability analysis of a haptic system where local dynamics are described by some second-order mechanical dynamics is presented. Next, using two optimization techniques ( and stability, margin optimization) an optimal choice for the controller gains is proposed. The derived results are tested on a three degree-of-freedom real-time experimental platform to illustrate the theoretical results. [Copyright &y& Elsevier]