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Journal ArticleDOI

Some generalizations of positive definiteness and monotonicity

Miroslav Fiedler, +1 more
- 01 Dec 1966 - 
- Vol. 9, Iss: 2, pp 163-172
About: 
This article is published in Numerische Mathematik.The article was published on 1966-12-01. It has received 208 citations till now. The article focuses on the topics: Positive definiteness.

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Linear Matrix Inequalities in System and Control Theory

Edwin E. Yaz
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Journal ArticleDOI

Complementary pivot theory of mathematical programming

Richard W. Cottle, +1 more
- 01 Apr 1967 - 
TL;DR: The role of problems of the form w and z satisfying w = q + Mz, w = or 0, z = or0, zw = 0 play a fundamental role in mathematical programming.
Journal ArticleDOI

New conditions for global stability of neural networks with application to linear and quadratic programming problems

Mauro Forti, +1 more
- 01 Jul 1995 - 
TL;DR: In this paper, the authors present new conditions ensuring existence, uniqueness, and global asymptotic stability of the equilibrium point for a large class of neural networks, which are applicable to both symmetric and nonsymmetric interconnection matrices and allow for the consideration of all continuous non-reasing neuron activation functions.
Journal ArticleDOI

Global convergence of neural networks with discontinuous neuron activations

Mauro Forti, +1 more
- 03 Nov 2003 - 
TL;DR: Results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov are employed, and global convergence is addressed by using a Lyapunov-like approach based on the concept of monotone trajectories of a differential inclusion.
Book ChapterDOI

Structured and Simultaneous Lyapunov Functions for System Stability Problems

Stephen Boyd, +1 more
- 01 Jun 1989 - 
TL;DR: Boyd and Yang as mentioned in this paper showed that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of x = Ax for some appropriate A.