Journal ArticleDOI
An alternative proof of the Barker, Berman, Plemmons (BBP) result on diagonal stability and extensions
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TLDR
In this article, the authors revisited the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system.About:
This article is published in Linear Algebra and its Applications.The article was published on 2009-01-01. It has received 60 citations till now. The article focuses on the topics: Diagonal & Lyapunov equation.read more
Citations
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Journal ArticleDOI
Robust stability and stabilization of uncertain linear positive systems via integral linear constraints : L-1-gain and L-infinity-gain characterization
TL;DR: Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems and the obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's Theorem.
Journal ArticleDOI
The Bounded Real Lemma for Internally Positive Systems and H-Infinity Structured Static State Feedback
Takashi Tanaka,Cedric Langbort +1 more
TL;DR: The bounded real lemma for internally positive linear time-invariant systems is considered and it is shown that the H∞ norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function.
Journal ArticleDOI
Brief paper: Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws
TL;DR: Explicit boundary dissipative conditions are given for the exponential stability in L^2-norm of one-dimensional linear hyperbolic systems of balance laws when the matrix M is marginally diagonally stable.
Journal ArticleDOI
LMI approach to linear positive system analysis and synthesis
TL;DR: It is shown that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument and a new LMI is derived for the H ∞ performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric.
Proceedings ArticleDOI
Optimal L 1 -controller synthesis for positive systems and its robustness properties
TL;DR: This paper shows that an L1-optimal state-feedback gain designed for a fixed positive system and a fixed pair of weighing vectors is robustly optimal against variations on the input matrix, the direct feedthrough matrix of the controlled positive system as well as variations onThe weighting vector for the disturbance input signal.
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Book
Positive Linear Systems: Theory and Applications
Lorenzo Farina,Sergio Rinaldi +1 more
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.
Book
Completely Positive Matrices
TL;DR: In this article, the PSD Completion Problem Complete Positivity: Definition and Basic Properties Cones of Completely Positive Matrices Small Matrices complete positive matrix Small matrices complete positivity and the comparison matrix Completely positive graphs complete positive graph matrix complete positive graphs complete positive matrices of a given rank Complete positive matrix of the graph.
Book
Matrix diagonal stability in systems and computation
Eugenius Kaszkurewicz,Amit Bhaya +1 more
TL;DR: In this paper, the authors provide a reference for methods and analysis to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations and provide a framework for the analysis of such systems.
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