Results 221 to 230 of about 8,061 (255)

Uniform asymptotic stability of a singularly perturbed system via the Lyapunov matrix-function

Nonlinear Analysis: Theory, Methods & Applications, 1987
For the singularly perturbed system \[ (1)\quad \frac{dx}{dt}=f(t,x,y),\quad \mu \frac{dy}{dt}=g(t,x,y,\mu) \] a generalization of the direct Lyapunov method on the basis of the concept of matrix function is suggested. The application of matrix functions allows the author a) to extend the class of functions appropriate for the construction of a scalar ...
exaly   +3 more sources

Matrix-Valued Lyapunov Function for an Extended Dynamic System

International Applied Mechanics, 2001
A new method is proposed to construct a matrix-valued Lyapunov function for a linear autonomous system extended in accordance with the Ikeda–Siljak ...
A. A. Martynyuk, V. I. Slyn'ko
openaire   +1 more source

Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems

2002
We consider linear systems of differential equations \(I\ddot x + B\dot x + Cx = 0\) where I is the identity matrix and B and C are general complex n x n matrices. Our main interest is to determine conditions for complete marginal stability of these systems.
Wolfhard Kliem, Christian Pommer
openaire   +1 more source

On application of the Lyapunov matrix-functions in the theory of stability

Nonlinear Analysis: Theory, Methods & Applications, 1985
We consider the differential equation (1) \(\dot x=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f\in C(R_+\times R^ n)\). Suppose that the solution \(\chi (t;x_ 0)\) of system (1) is unique and exists for all \(t\geq 0\) for \(t_ 0\geq 0\), \(x_ 0\in int N\), \(N\subseteq R^ n\), \(\chi (t_ 0,x_ 0)=x_ 0\).
openaire   +1 more source

A polytopic quadratic Lyapunov functions approach to stability of a matrix polytope

29th IEEE Conference on Decision and Control, 1990
It is known that a polytope of matrices is stable if there exists a positive-definite quadratic function that is a Lyapunov function common to all the vertex members. This simple criterion is extended to the case where a multituple of positive-definite quadratic functions is available.
H. Kokame, H. Kida, T. Mori
openaire   +1 more source

Synthesis of discretized Lyapunov functional method and the Lyapunov matrix approach for linear time delay systems

Automatica
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Irina V. Alexandrova, Aleksandr I. Belov
openaire   +2 more sources

Instability conditions for linear time delay systems: a Lyapunov matrix function approach

International Journal of Control, 2011
Instability conditions for linear time delay systems of retarded type, with distributed delay, and of neutral type are given. The approach is based on using the converse results on the existence of special quadratics lower bounds for the Lyapunov–Krasovskii functional of complete type associated to these systems.
Sabine Mondié, Gilberto Ochoa, Blanca M. Ochoa   +2 more
openaire   +1 more source

Absolute stability of a singularly perturbed Lur'e system and Lyapunov's matrix function

Soviet Applied Mechanics, 1987
In this paper [which is a continuation of the first author's article in e.g.: Dokl. Akad. Nauk SSSR 287, 786-789 (1986; Zbl 0611.34047)] the stability of a singularly perturbed system of the Lur'e form is analyzed on the basis of the Lyapunov matrix function (LMF). We obtain sufficient conditions for the absolute stability of a system of the Lur'e form
Martynyuk, A. A., Miladzhanov, V. G.
openaire   +2 more sources

Matrix Lyapunov functions method for sets of dynamic equations on time scales

Nonlinear Analysis: Hybrid Systems, 2019
Stability theory of set diferential equations on time scales is studied. The definition of a regressive set valued map on a time scale (Definition 2.6) involves an addition operation between a scalar and an element of \(\mathbb{K}_c(\mathbb{R}^n)\), the function \(\Theta X(t)\) given in Definition 2.7 includes a quotient of two elements of \(\mathbb{K ...
Martynyuk, A. A., Stamova, I. M., Martynyuk-Chernienko, Yu. A.   +2 more
openaire   +2 more sources

Lyapunov-type functions and invariant sets for Riccati matrix differential equations

1997 European Control Conference (ECC), 1997
We present two different methods to obtain global existence results for solutions of nonsymmetric Riccati matrix differential equations. In the first approach we derive sufficient conditions ensuring that the spectral norm of the solutions remains uniformly bounded in an interval (−∞, to]: in a second part we make use of the linearizability of the ...
G. Freiling, G. Jank, A. Sarychev
openaire   +1 more source