Yassine Ariba

An augmented model for robust stability analysis of time-varying delay systems

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modelling of the delay system. New types of Lyapunov–Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay-dependent stability conditions are then formulated in terms of linear matrix inequalities. Finally, several examples show the effectiveness of the proposed methodology.

Delay-dependent stability analysis of linear systems with time-varying delay

Stability analysis of linear systems with time- varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, an example shows the effectiveness of the proposed methodology.

Stability interval for time-varying delay systems

We investigate the stability analysis of linear time-delay systems. The time-delay is assumed to be a time-varying continuous function belonging to an interval (possibly excluding zero) with a bound on its derivative. To this end, we propose to use the quadratic separation framework to assess the intervals on the delay that preserves the stability. Nevertheless, to take the time-varying nature of the delay into account, the quadratic separation principle has to be extended to cope with the general case of time-varying operators. The key idea lies in rewording the delay system as a feedback interconnection consisting of operators that characterize it. The original feature of this contribution is to design a set of additional auxiliary operators that enhance the system modelling and reduce the conservatism of the methodology. Then, separation conditions lead to linear matrix inequality conditions which can be efficiently solved with available semi-definite programming algorithms. The paper concludes with illustrative academic examples.

Delay range stability of a class of distributed time delay systems

This paper is dedicated to the stability analysis of a class of uncertain distributed delay systems, the kernel of which can be modeled as a polynomial function of the delay. The results are constructed by rewriting the system as an uncertain interconnected model. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. To this end, some relations that highlight relevant characteristics of the delayed term are added to the interconnected model leading then to the conservatism reduction. Finally, numerical examples show the effectiveness of the proposed method.

On designing Lyapunov-Krasovskii based AQM for routers supporting TCP flows

For the last few years, we assist to a growing interest of designing AQM (active queue management) using control theory. In this paper, we focus on the synthesis of an AQM based on the Lyapunov theory for time delay systems. With the help of a recently developed Lyapunov-Krasovskii functional and using a state space representation of a linearized fluid model of TCP, two robust AQMs stabilizing the TCP model are constructed. Notice that our results are constructive and the synthesis problem is reduced to a convex optimization scheme expressed in terms of linear matrix inequalities (LMIs). Finally, an example extracted from the literature and simulations via NS simulator [Fall, K., et al., www.isi.edu/nsnam/ns/] support our study.

Delay Range Stability of Distributed Time Delay Systems

Abstract This paper is dedicated to the stability analysis of a class of uncertain distributed delay systems, the kernel of which can be modeled as a polynomial function. The results are constructed by rewriting the system as an uncertain interconnected model. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. To this end, some relations that highlight relevant characteristics of the delayed term are added to the interconnected model leading then to the conservatism reduction. Finally, numerical examples show the effectiveness of the proposed method.

Simple conditions for L2 stability and stabilization of networked control systems

Abstract The stability analysis and stabilization of networked control systems subject to data loss and time-varying transmission delays are explored. The stability result is based on quadratic separation and operator theory, which allows to capture the above phenomena into the single formalism of aperiodic sampling. The obtained stability condition is expressed through an LMI. The stabilization problem is a bit more involved due to the inherent structure of the obtained LMI. An approximation (dilation) is then proposed to obtain a more tractable LMI for stabilization. Several examples illustrate the effectiveness of the proposed approach.

Bessel inequality for robust stability analysis of time-delay system

This paper addresses the problem of the stability analysis for a linear time-delay systems via a robust analysis approach and especially the quadratic separation framework. To this end, we use the Bessel inequality for building operators that depend on the delay. They not only allow us to model the system as an uncertain feedback system but also to control the accuracy of the approximations made. Then, a set of LMIs conditions are proposed which tends on examples to the analytical bounds for both delay dependent stability and delay range stability.

Optimal Control Strategies for Load Carrying Drones

This chapter studies control strategies for load carrying drones. Load carrying drones not only have to fly in a cooperative way, but also are mechanically interconnected. Due to these characteristics, the control problem is an interesting and challenging issue to deal with. Throughout this chapter, a dynamic model based on first principle is developed. To that end, it is proposed to model this system as a ball and beam system lifted by two drones. Afterwards, different control techniques are implemented and compared by simulations. Specifically, linear-quadratic regulator (LQR) and model predictive control (MPC) are studied. Both control techniques belong to the optimal control methodology. This comparison is interesting since LQR permits to perform an optimal control law with short execution times, while MPC deals with physical constraints and predictions, being the execution time and the physical constraints important issues to handle in this kind of systems. Finally, simulation results and open issues are discussed.

Control over a Hybrid MAC Wireless Network

Wireless Sensor Networks and Control Systems are an essential part of the Smart Grid. We consider the problem of performing control over large complex networked systems with packet drops. More specifically, we are interested in improving the performance of the regulation of control loops when the communication is made over low-cost wireless networks. In control over wireless networks it is common to use Contention-Free (CF) schemes where no losses occur with the price of low scalability and complicated scheduling policies. In this work we propose a hybrid MAC and control architecture, where a small number of control loops with high demand of attention are scheduled in a CF scheme and well regulated loops are scheduled in a lossy, asynchronous and highly scalable, Contention-Access (CA) scheme. We model and analyze the performance of such system with Markov Jump Linear System (MJLS) tools and compare it with other architecture types. Performance is evaluated using a quadratic cost function of the state.