Topic
Positive systems
About: Positive systems is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21405 citations.
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01 Jun 2000
TL;DR: In this article, the authors define and define conditions of positivity of equilibria, including reachability and observability, and define a set of conditions for positive equilibrium. But they do not define the conditions of transparency.
Abstract: DEFINITIONS. Definitions and Conditions of Positivity. Influence Graphs. Irreducibility, Excitability and Transparency. PROPERTIES. Stability. Spectral Characterization of Irreducible Systems. Positivity of Equilibria. Reachability and Observability. Realization. Minimum Phase. Interconnected Systems. APPLICATIONS. Input-Output Analysis. Age-Structured Population Models. Markov Chains. Compartmental Systems. Queueing Systems. Conclusions. Annotated Bibliography. Bibliography. Appendices. Index.
1,957 citations
TL;DR: It is shown that the theory of nonnegative matrices may be employed to model communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms and these results can be used to develop tools for analyzing the behavior of AIMD communication networks.
Abstract: We study communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms. It is shown that the theory of nonnegative matrices may be employed to model such networks. In particular, important network properties, such as: 1) fairness; 2) rate of convergence; and 3) throughput, can be characterized by certain nonnegative matrices. We demonstrate that these results can be used to develop tools for analyzing the behavior of AIMD communication networks. The accuracy of the models is demonstrated by several NS studies.
480 citations
TL;DR: The synthesis of state-feedback controllers is solved in terms of linear programming problem, including the requirement of positiveness of the controller and its extension to uncertain plants.
Abstract: This brief solves some synthesis problems for a class of linear systems for which the state takes nonnegative values whenever the initial conditions are nonnegative. In particular, the synthesis of state-feedback controllers is solved in terms of linear programming problem, including the requirement of positiveness of the controller and its extension to uncertain plants. In addition, the synthesis problem with nonsymmetrical bounds on the stabilizing control is treated
424 citations
TL;DR: This work presents a necessary and sufficient condition for the existence of a common linear copositive Lyapunov function existence for switched systems with two constituent linear time-invariant systems.
Abstract: We consider the problem of common linear copositive Lyapunov function existence for positive switched linear systems. In particular, we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time-invariant systems. Several applications of this result are also given.
405 citations
TL;DR: Using linear co-positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented and applied to a simplified human immunodeficiency viral mutation model.
Abstract: This paper has been motivated by the problem of viral mutation in HIV infection. Under simplifying assumptions, viral mutation treatment dynamics can be viewed as a positive switched linear system. Using linear co-positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented. These results are then applied to a simplified human immunodeficiency viral mutation model. The optimal switching control law is compared with the law obtained through an easily computable guaranteed cost function. Simulation results show the effectiveness of these methods. Copyright © 2010 John Wiley & Sons, Ltd.
349 citations