Calculation of Quadratic Moments of High-Order Linear Systems via Routh Canonical Transformation
- 1 November 1964
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Applications and Industry
- Vol. 83 (75), 428-433
- https://doi.org/10.1109/tai.1964.5407717
Abstract
In this paper, three different methods are developed for calculating various moments of the system variables of a linear system, represented by matrix equation x = Ax. A transformation Q is developed which transforms the system matrix A into a special matrix R. Liapunov function V is considered as V = xtQtQx and it facilitates evaluation of various moments ∫0∞ tmx2dt These methods are especially useful for high-order systems. Examples are included to explain each method.Keywords
This publication has 4 references indexed in Scilit:
- Comment on "A new proof of the Routh-Hurwitz stability criterion by the second method of Lyapunov with applications to optimum transfer functions"IEEE Transactions on Automatic Control, 1964
- Second method of Liapunov and Routh's canonical formJournal of the Franklin Institute, 1963
- THE CALCULATION OF FUNCTIONALS OF THE TIME AND FREQUENCY RESPONSE OF A LINEAR CONSTANT COEFFICIENT DYNAMICAL SYSTEMThe Quarterly Journal of Mechanics and Applied Mathematics, 1963
- Control system analysis and design via the second method of lyapunov: (I) continuous-time systems (II) discrete time systemsIRE Transactions on Automatic Control, 1959