Results 211 to 220 of about 742,320 (261)

Construction of Delay Lyapunov Matrix for Integral Delay Systems

2018 IEEE Conference on Decision and Control (CDC), 2018
The construction of Lyapunov matrices for integral delay systems with constant and exponential kernel are presented. It is reduced to the solutions of a matrix delay free system subject to boundary conditions. The results are validated by testing known necessary stability conditions in terms of the Lyapunov matrix.
Reynaldo Ortiz, Sabine Mondie, Saul Del Valle, Alexey V. Egorov   +3 more
openaire   +1 more source

Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems

Journal of Mechanical Design, 1995
Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given.
D.S. Bernstein, S.P. Bhat
openaire   +1 more source

Extended Dissipativity and Control Synthesis of Interval Type-2 Fuzzy Systems via Line-Integral Lyapunov Function

IEEE transactions on fuzzy systems, 2020
This article addresses the problems of the stability and extended dissipativity analysis and control synthesis for interval type-2 fuzzy systems. A sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration
Shaosheng Zhou, Yingying Han
semanticscholar   +1 more source

Lyapunov's matrix equation with system matrix in companion form

International Journal of Control, 1993
Abstract A simple method for solving Lyapunov's matrix equation for linear continuous systems with the system matrix in companion form is proposed. The method involves the inversion of the Hurwitz matrix. A necessary and sufficient condition for the existence of a solution to the equation is also obtained.
openaire   +1 more source

Solution of the Lyapunov matrix equation for a system with a time‐dependent stiffness matrix

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2003
AbstractThe stability of the linearized model of a rotor system with non‐symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces.
Pommer, Christian, Kliem, Wolfhard
openaire   +2 more sources

Lyapunov matrix of linear systems with delays: A polynomial approximation

2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2009
A polynomial approximation of the Lyapunov matrix appearing in the complete type Lyapunov Krasovskii functionals associated to time delay systems of retarded type with multiple arbitrary delays is proposed. Two measures of the quality of the approximation are provided: the first one is an estimate of the error in the derivative and the second one is ...
Erick Huesca, Sabine Mondie
openaire   +1 more source

Second-order n-dimensional systems and the Lyapunov matrix equation

IEEE Transactions on Automatic Control, 1971
Equations analogous to the Lyapunov matrix equation are derived for second-order n -dimensional systems. These are shown to be more readily solvable than the equivalent 2n -dimensional Lyapunov matrix equation.
J. Heinen, L. Crum
openaire   +1 more source

Solution of Lyapunov equation with system matrix in companion form

IEE Proceedings D Control Theory and Applications, 1991
The authors consider a method of solving the algebraic matrix Lyapunov equation \(AQ+QA^ T=-bb^ T\) where \(A,Q\) are \(n\times n\) matrices \((A\) is given) and \(b\) is an \(n\times 1\) vector. Assuming that the matrix \(A\) is in the companion form and \(b=(0,0,\ldots,0,1)^ T\), they describe an algorithm to find entries of matrix \(Q\) (provided ...
Sreeram, V., Agathoklis, P.
openaire   +2 more sources

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

The Lyapunov matrix-function and stability of hybrid systems

Nonlinear Analysis: Theory, Methods & Applications, 1986
The concept of matrix Lyapunov function (not to be confused with scalar function presented in vector-matrix form) is applied to the investigation of the stability of the isolated equilibrium state of hybrid systems. This approach allows one to universalize the procedure of construction of the appropriate Lyapunov function and to find an algorithm for ...
openaire   +2 more sources