Results 221 to 230 of about 10,834,365 (253)

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
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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.
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Stability and the matrix Lyapunov equation for delay differential systems

International Journal of Control, 1989
Abstract Asymptotic stability independent of the delay of linear differential delay systems with commensurate and non-commensurate delays is analysed using 2-D (two-dimensional) and n-D (n-dimensional) state-space models. Sufficient conditions for stability are obtained in terms of the frequency dependent 1-D (one-dimensional) Lyapunov equations.
P. Agathoklis, S. Foda
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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
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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 ...
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Estimate for the root-location of linear systems via the lyapunov matrix equation

Journal of the Franklin Institute, 1982
Abstract It is well known that the Lyapunov matrix equation can be utilized to obtain the estimate for the transient behavior of linear constant systems. This paper shows that the equation gives information not only on the maximum real part of the characteristic roots of system matrix but also on other extremal values to these roots.
Mori, Takehiro, Kuwahara, Michiyoshi, Fukuma, Norio   +2 more
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The Lyapunov matrix function and the stability of hybrid systems

Soviet Applied Mechanics, 1985
The purpose of the present article is to solve the problem of the stability of the equilibrium state of a hybrid (complex) system \(\Sigma\) consisting of a number of rigid, elastic, and liquid substances, related by connecting functions. The subsystems include both stable and unstable ones and the stability of the equilibrium state of the entire ...
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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
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Stability and the matrix Lyapunov equation for differential systems with delays

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 2005
The author establishes sufficient conditions for the stability of linear and time-variant delay differential systems including their various usual subclasses (i.e., point, distributed, and mixed point-distributed delay systems). Sufficient conditions for stability are obtained in terms of the Schur complement of operators and the frequency-domain ...
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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
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