Positive Linear Systems: Theory and Applications

By Lorenzo Farina, Sergio Rinaldi. 2000

2,260 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/fff5198085e7975f3a4a2fa57f75a646d8156da9

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In Control and Systems Engineering

Citations in the corpus

Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems (2005, background): “The first result appears in [16,31]and is stated here for completeness.”
Minimal positive realizations of transfer functions with positive real poles (2000, background): “systems(see, for general overviews, [17], [16], and [9]).”
Stability Criteria for Switched and Hybrid Systems (2007, background): “A different type of constraint arises in the study of positive switched linear systems, where any trajectory starting from nonnegative initial conditions must remain within the nonnegative orthant for all subsequent times [48, 95].”
Structural properties of positive linear time-invariant difference-algebraic equations (2002, background): “A complete introduction to positive linear standard systems can be found in [7].”
Controller Synthesis for Positive Linear Systems With Bounded Controls (2007, background): “In the literature, such systems are referred to be positive (see [4], [8], [11], and [14] for general references).”
Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization (2013, background): “Positive interconnections are recurrent in the analysis of positive systems and have already been considered in several works [4,12,32,40].”
Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays (2019, background): “Such systems can be found in many fields such as industrial engineering [1], biomedicine [2,3], network communication [4], and air traffic management [5].”
Positive electrical circuits and their reachability (2011, background): “[2, 5] The system (1) is positive if and only if .”
Stability of switched positive nonlinear systems (2016, background): “For example, they are D-stable, meaning that global asymptotical stability is preserved under diagonal scaling [1].”
Monotone control systems (2002, background): “attention in the control literature; see, for instance, [7], [10], [19], [21], [22], and [31].”
Global attractivity, I/O monotone small-gain theorems, and biological delay systems (2005, positive): “The topic of monotone and related positive systems is a very active current area of research, especially in biological applications; see e.g. [1] [5] [12] [11] [27].”
Practical stability and asymptotic stability of positive fractional 2D linear systems (2009, background): “An overview of state of the art in positive systems theory is given in the monographs [1, 2].”
Robust stability of positive discrete-time linear systems of fractional order (2010, background): “An overview of state of the art in positive systems theory is given in the monographs [1, 2].”
Computation of realizations of discrete-time cone-systems (2006, methodology): “Realizations problem of positive linear systems without timedelays has been considered in many papers and books [1,2,5].”