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Positive Linear Systems: Theory and Applications
Lorenzo Farina,Sergio Rinaldi +1 more
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TLDR
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.read more
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Journal ArticleDOI
Stability Criteria for Switched and Hybrid Systems
TL;DR: This paper considers the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws, and discusses the theory of Lyapunov functions and the existence of converse theorems.
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Monotone control systems
David Angeli,Eduardo D. Sontag +1 more
TL;DR: In this paper, the notion of monotonicity is extended to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components.
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Brief paper: Stability of switched positive linear systems with average dwell time switching
TL;DR: The stability analysis problem for a class of switched positive linear systems (SPLSs) with average dwell time switching is investigated and a multiple linear copositive Lyapunov function is introduced, by which the sufficient stability criteria are given for the underlying systems in both continuous-time and discrete-time contexts.
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Controller Synthesis for Positive Linear Systems With Bounded Controls
Mustapha Ait Rami,Fernando Tadeo +1 more
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.
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On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems
Oliver Mason,Robert Shorten +1 more
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.