Results 181 to 190 of about 5,561 (210)
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Solution of Lyapunov equation with system matrix in companion form
IEE Proceedings D Control Theory and Applications, 1991The 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, 1989Abstract 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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Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems
2002We 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
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Matrix-Valued Lyapunov Function for an Extended Dynamic System
International Applied Mechanics, 2001A 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, 1986The 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, 1982Abstract 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 +2 more
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The Lyapunov matrix function and the stability of hybrid systems
Soviet Applied Mechanics, 1985The 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, 1995Necessary 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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Analytical construction of the hierarchical matrix Lyapunov function for impulse systems
Ukrainian Mathematical Journal, 1997See the review in Zbl 0887.93062.
Martynyuk, A. A., Begmuratov, K. A.
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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, 2005The 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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