Quadratic Separation Framework Research Articles

Input/output stability of a damped string equation coupled with ordinary differential system

SummaryThe input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time‐delay systems, an exact stability result is firstly derived using pole locations. Then, based on the small‐gain theorem and on the quadratic separation framework, some robust stability criteria are provided. The latter follows from a projection of the infinite dimensional system states onto an orthogonal basis of Legendre polynomials. Numerical examples comparing these results with the ones in the literature are presented along with demonstrations of the effectiveness of the developed robust stability criteria.

Quadratic separation framework for stability analysis of a class of systems with time delays

This paper is concerned with the stability analysis of a class of systems with time delays through a kind of Quadratic Separation (QS) Framework. A novel method for the construction of Integral Quadratic Constraints (IQCs) that will be used in the QS framework is proposed. A unified framework is proposed based on the QS theory and the Lyapunov theory, and then is applied to the stability analysis of linear systems with time delays. Stability criteria are established based on the proposed approach. Numerical examples are finally provided to show its effectiveness.

New Absolute Stability Conditions of Lur’e Systems with Time-Varying Delay

This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.

Improved stability criteria of static recurrent neural networks with a time-varying delay.

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

Feedback control for router management and TCP/IP network stability

Several works have established links between congestion control in communication networks and feedback control theory. In this paper, following this paradigm, the design of an AQM (active queue management) ensuring the stability of the congestion phenomenon at a router is proposed. To this end, a modified fluid flow model of TCP (transmission control protocol) that takes into account all delays of the topology is introduced. Then, appropriate tools from control theory are used to address the stability issue and to cope with the time-varying nature of the multiple delays. More precisely, the design of the AQM is formulated as a structured state feedback for multiple time delay systems through the quadratic separation framework. The objective of this mechanism is to ensure the regulation of the queue size of the congested router as well as flow rates to a prescribed level. Furthermore, the proposed methodology allows to set arbitrarily the QoS (quality of service) of the communications following through the controlled router. Finally, a numerical example and some simulations support the exposed theory.

DELAY-DEPENDENT STABILITY ANALYSIS OF LINEAR TIME DELAY SYSTEMS

AbstractStability of time delay systems is investigated considering the delay-dependent case. The system without delays is assumed stable and conservative conditions are derived for finding the maximal delay that preserves stability. The problem is treated in the quadratic separation framework and the resulting criteria are formulated as feasibility problems of Linear Matrix Inequalities. The construction of the results relies on a fractioning of the delay. As the fractioning becomes thinner, the results prove to be less and less conservative. An example show the effectiveness of the proposed technique.