Positive 1D and 2D Systems

By J. Rigelsford. 2002

470 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8edc9afb4708978b8e6286d68f50a3c6d9d18ddf

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In Computational Theory and Mathematics

Citations in the corpus

Adaptive law with a new leakage term (2010, background): “3 is positive real (PR), H2 is SPR and u1(t) [ L2, then y1(t) [ L2’.”
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].”
On stability and stabilizability of positive delay systems (2009, background): “To mention a few, the stability problem of positive systems is investigated in [2–4], the control and stabilization problems are studied in [3, 7], the eigenvalue regions of positive systems are analyzed in [1], and so on (readers are referred to [3, 5] for a detailed account of the recent study on ”
Functional interval observer for the linear systems with disturbances (2018, background): “with the initial value x(t0) = x0, and due to the monotone system theory, all the solutions of (4) are non-negative, namely x(t) ≥ 0 for t ≥ t0 [35].”
Stability Analysis of Positive Switched Linear Systems With Delays (2011, background): “A positive system implies that its states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative [14], [15].”
Controllability of dynamical systems. A survey (2013, methodology): “Mathematical fundamentals of fractional calculus and fractional differential and difference equations are given in the monographs [60], and in the related papers [55-59].”
Asymptotic stability of positive 2D linear systems with delays (2009, background): “An overview of 2D linear systems theory is given in [9–13], and some recent result in positive systems has been given in monographs [8, 14].”
Stability analysis of positive descriptor systems (2008, background): “Very little is known about positive descriptor systems up to now, however, some properties mainly in the discrete-time case were studied in [10,11,12,26].”
Decay rate constrained stabilization of positive systems using static output feedback (2011, methodology): “Figures 1 and 2 describe, respectively, the state variable trajectories for the open-loop system ẋ(t)= AM x(t) and the closed-loop system ẋ(t)= (A+BLC)x(t) under the same initial condition x(0)= [2 4 6]T.”
Stability of a class of switched positive linear time‐delay systems (2013, background): “It is noted that the non-negativity of each state vector element for all times of positive systems will bring about some difficulties, which cannot be solved by using well-developed methods for general linear systems [2, 11, 13].”
Stability of switched positive linear systems with average dwell time switching (2012, background): “In particular, positive linear systems have drawn considerable interest due to their numerous applications in the areas such as economics, biology, communications, etc. (Benvenuti & Farina, 2004; Kaczorek, 2002; Rami, 2011).”
Simple stability conditions for linear positive discrete-time systems with delays (2008, background): “An overview of state of the art in positive systems theory is given in the monographs [1, 2].”
Practical stability of positive fractional discrete-time linear systems (2008, background): “An overview of state of the art in positive systems theory is given in monographs [1, 2].”
Distributed control of positive systems (2011, unknown): “Positive systems have also been studied in the control literature [23,6,10], and increasingly so during the last decade.”