Journal ArticleDOI
Stability regions of large-scale systems
TLDR
In this article, three different forms of Liapunov functions are used for describing the stability behavior of the aggregated system, but one form in particular, heretofore not used in this context, is found to be the most natural.About:
This article is published in Automatica.The article was published on 1973-11-01. It has received 91 citations till now. The article focuses on the topics: Exponential stability & Stability (probability).read more
Citations
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Journal ArticleDOI
Vector norms as Lyapunov functions for linear systems
TL;DR: A unified theory of quadratic and piecewise-linear Lyapunov functions for continuous and discrete-time linear systems is presented and sufficient and necessary conditions for a vector norm to be a Lyap unov function are presented.
Journal ArticleDOI
Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices
TL;DR: In this article, the composite-system method for analyzing stability of large-scale system is studied focusing on the quadratic-order theorems using M -matrices, and the results are generally useful for stability analysis of multi-input multi-output systems.
Journal ArticleDOI
Asymptotic stability and instability of large-scale systems
TL;DR: In this paper, the authors extended the application of Lyapunov's theory to stability analysis of large-scale dynamic systems by redefining interconnection functions among the subsystems according to interconnection matrices, which can be used to determine connective asymptotic stability of large scale systems under arbitrary structural perturbations.
Journal ArticleDOI
Output feedback variable structure control design
TL;DR: This paper describes a procedure for variable structure output feedback control (VSOFC) for a class of multivariable linear time-invariant systems and introduces two switching surface design algorithms based on both a static output feedback and on an eigenstructure assignment techniques.
Journal ArticleDOI
Design of stabilizing switching control laws for discrete- and continuous-time linear systems using piecewise-linear Lyapunov functions
TL;DR: In this paper, the stability of switched linear systems is investigated using piecewise linear Lyapunov functions, and the authors identify classes of switching sequences that result in stable trajectories.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
On matrices with non-positive off-diagonal elements and positive principal minors
Miroslav Fiedler,Vlastimil Pták +1 more
Journal ArticleDOI
Finite time stability under perturbing forces and on product spaces
Leonard Weiss,E. F. Infante +1 more
TL;DR: In this article, a qualitative theory of stability for non-autonomous systems operating over finite time intervals has been developed, and sufficient conditions are given for various types of finite time stability of a system under the influence of perturbing forces which enter the system equations linearly.