๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Second method of Liapunov and Routh's canonical form

โœ Scribed by N.N. Puri; C.N. Weygandt

Publisher
Elsevier Science
Year
1963
Tongue
English
Weight
626 KB
Volume
276
Category
Article
ISSN
0016-0032

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper the equivalence between Liapunov's Second Method and the Routh-Hurwitz Criterion for Linear Systems is established. A transformation matrix Q is developed which transforms the system matrix A into a special matrix R called ~t Routh Canonical matrix. The element~ of R matrix are closely related to the elements iu the first column of Routh's arrays. The conditions of ~tability on R matrix from Liapunov's Second Method are the same as the Routh-Hurwitz Conditioa~. The treatment is extended to nonlinear systems. As a result of this transformation, the linear terms are automatically removed from further consideration and only the nonlinear terms remain. Method of analysis is explained with the help of examples.

๐Ÿ“œ SIMILAR VOLUMES

On the second method of liapunov
On the second method of liapunov
โœ S.K Persidskii ๐Ÿ“‚ Article ๐Ÿ“… 1961 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 463 KB
Stability studies for a class of nonline
Stability studies for a class of nonlinear difference equations using Liapunov's Second Method
โœ N.N. Puri; R.L. Drake ๐Ÿ“‚ Article ๐Ÿ“… 1965 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 461 KB

In this paper a discrete analogue of Liapunov Direct Method is applied to the stability analysis of nonlinear, nonautonomous diflerence equations. A class of second and third order equations are analyzed. The Liapunov functions are generated by the use of a Routh canonical transformation. Concrete e