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Quadratic and Copositive Lyapunov Functions and the Stability of Positive Switched Linear Systems
, 2007
"... We present some new results concerning the stability of positive switched linear systems. In particular, we present a necessary and suf£cient condition for the existence of copositive linear Lyapunov functions for switched systems with two constituent linear timeinvariant (LTI) systems. We also e ..."
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We present some new results concerning the stability of positive switched linear systems. In particular, we present a necessary and suf£cient condition for the existence of copositive linear Lyapunov functions for switched systems with two constituent linear timeinvariant (LTI) systems. We also extend some recent results on quadratic stability for positive switched linear systems.
An LMI approach to checking stability of 2D positive systems
 Bull. Pol. Ac.: Tech
, 2007
"... Abstract. Twodimensional (2D) positive systems are 2D statespace models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient ..."
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Cited by 4 (0 self)
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Abstract. Twodimensional (2D) positive systems are 2D statespace models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both FornasiniMarchesini models (FFMM and SFMM) and for the general model. 1.
1 Modelling TCP Dynamics in Wireless Networks
"... Abstract — In this paper we develop an analytic model of the behaviour of competing TCP flows in wireless networks. A key feature of this work is that we take explicit account of the interactions between competing TCP flows. This allows us to study issues such as responsiveness and the impact of the ..."
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Abstract — In this paper we develop an analytic model of the behaviour of competing TCP flows in wireless networks. A key feature of this work is that we take explicit account of the interactions between competing TCP flows. This allows us to study issues such as responsiveness and the impact of the flow AIMD parameters on fairness.
Congestion Control using Efficient Explicit Feedback
 in Proc. INFOCOM
, 2009
"... Abstract—This paper proposes a framework for congestion control, called Binary Marking Congestion Control (BMCC) for high bandwidthdelay product networks. The basic components of BMCC are i) a packet marking scheme for obtaining high resolution congestion estimates using the existing bits available ..."
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Abstract—This paper proposes a framework for congestion control, called Binary Marking Congestion Control (BMCC) for high bandwidthdelay product networks. The basic components of BMCC are i) a packet marking scheme for obtaining high resolution congestion estimates using the existing bits available in the IP header for Explicit Congestion Notification (ECN) and ii) a set of loaddependent control laws that use these congestion estimates to achieve efficient and fair bandwidth allocations on high bandwidthdelay product networks, while maintaining a low persistent queue length and negligible packet loss rate. We present analytical models that predict and provide insights into the convergence properties of the protocol. Using extensive packetlevel simulations, we assess the efficacy of BMCC and perform comparisons with several proposed schemes. BMCC outperforms VCP, MLCP, XCP, SACK+RED/ECN and in some cases RCP, in terms of average flow completion times for typical Internet flow sizes. I.
Stability and stabilizability of special classes of discretetime positive switched systems
, 2011
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Modeling TCP in smallbuffer networks
, 2008
"... Abstract. Today, the large packet buffers present in backbone routers significantly increase their power consumption and design time. Recent models of networks with large buffers have suggested that these large buffers could be replaced with much smaller ones. Unfortunately, it turns out that these ..."
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Abstract. Today, the large packet buffers present in backbone routers significantly increase their power consumption and design time. Recent models of networks with large buffers have suggested that these large buffers could be replaced with much smaller ones. Unfortunately, it turns out that these models are not valid anymore in networks with small buffers, and therefore cannot predict how these smallbuffer networks will behave. In this paper, we introduce a new model that provides a complete statistical description of smallbuffer Internet networks. First, we present novel models of the distributions of several network components, such as the line occupancies of each flow, the instantaneous arrival rates to the bottleneck queues, and the bottleneck queue sizes. Then, we combine all these models in a single fixedpoint algorithm that forms the key to the global statistical smallbuffer network model. In particular, given some QoS requirements, this new model can be used to precisely size small buffers in backbone router designs. Keywords: SmallBuffer Network, Network Model, Backbone Routers. 1
SmallBuffer Networks
"... Today, because of TCP dynamics, Internet backbone routers hold large packet buffers, which significantly increase their power consumption and design time. Recent models of largebuffer networks have suggested that these large buffers could be replaced with much smaller ones. Unfortunately, it turns ..."
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Today, because of TCP dynamics, Internet backbone routers hold large packet buffers, which significantly increase their power consumption and design time. Recent models of largebuffer networks have suggested that these large buffers could be replaced with much smaller ones. Unfortunately, it turns out that these largebuffer network models are not valid anymore in smallbuffer networks, and therefore cannot predict how these smallbuffer networks will behave. In this paper, we introduce a new model that provides a complete statistical description of smallbuffer Internet networks. We present novel models of the distributions of several network components, such as the line occupancies of each flow, the instantaneous arrival rates to the bottleneck queues, and the bottleneck queue sizes. Later, we combine all these models in a single fixedpoint algorithm that forms the key to a global statistical smallbuffer network model. In particular, given some QoS requirements, we show how this new model can be used to precisely size small buffers in backbone router designs. Key words: SmallBuffer Network, Network Model, Backbone Routers. 1
Tools for the analysis and design of communication networks with markovian dynamics,” to appear
 in Proceedings of IEE, Control Theory and Applications
, 2005
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