Stability theory for nonnegative and compartmental dynamical systems with time delay

By Wassim M. Haddad, V. Chellaboina. Proceedings of the 2004 American Control Conference, 2004

331 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ff8e09d16bc891da49a4da35b678ee5781921a79

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In Computer Networks and Communications

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Citations in the corpus

• Positive observation problem for linear time-delay positive systems (2007, background): “The rest of the proof is similar to the one in [ 9 , 4, 2]. }”
• Positive state‐bounding observer for positive interval continuous‐time systems with time delay (2012, methodology): “By applying Lemma 2 and taking a similar line in [31], the following result on the asymptotic stability of positive systems in (1) is straightforward, and its proof is omitted here.”
• Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization (2013, background): “4 that the consideration of such scalings leads to a necessary and sufficient condition for the stability of positive time-delay systems with constant delays, recovering then the results of [48].”
• Exponential stability analysis for positive systems with delays (2011, background): “In contrast, for positive linear time-delay systems, it has been shown that the presence of constant delays does not affect the stability performance of the system [10-13].”
• Technical (1960, unknown): “2 Related Work”
• D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems (2010, background): “delay if the system with is GAS, thus extending the main result of [4] to a broad class of nonlinear systems.”
• Stability Analysis and Synthesis for Linear Positive Systems with Time-Varying Delays (2009, background): “presence of constant delays does not affect the stability performance of the system [20, 21, 23] (see also recent works [6, 7, 13 , 16, 17]).”
• Stability of a class of switched positive linear time‐delay systems (2013, background): “To list a few, necessary and sufficient stability criteria for positive systems with constant delay are obtained in [6] by means of linear co-positive Lyapunov functional, which is a powerful tool for tackling positive systems [16, 18], sufficient stability conditions for delayed positive systems wi”
• Stability Analysis of Positive Switched Linear Systems With Delays (2011, background): “For example, their stability is not affected by delays [18]–[20].”
• Exponential L1 output tracking control for positive switched linear systems with time-varying delays (2014, methodology): “To list a few, a necessary and sufficient stability criterion for positive systems with constant delays is obtained in [31] by means of a linear co-positive Lyapunov functional [19,32].”
• On stability and stabilizability of positive delay systems (2009, methodology): “[8] investigated the stability problem for nonnegative and compartmental dynamical systems with time delay, and proposed some stability conditions in term of linear vector equation.”
• Stability of switched positive nonlinear systems (2016, background): “Another important property is that their stability is independent of system delays [2].”