Construction of liapunov functions

✍ Scribed by Chiou-Shiun Chen; Edwin Kinnen

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 802 KB
• Volume: 289
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(70)90299-1

✦ Synopsis

An algorithm k presented for a vector

h which converts a given differential equution with polynomial nonlinearities into an autiliarg exact differential equation. The solution of the latter ia a Lhpunov function for the original equation. The vector h is equated to the cum of an undeterkned scalar function I/(X) and a second vector that is derived from the original differential equation. It is shown that #(x) can be developed sequentially; a unique h, an auxiliary exact differential equation and a Liapunov function may then be determined. T& procedure ia particularly uaeful for routinely developing a Lkpunov function for an unfamiliar equation to indicate either global atability or a nontrivial region of stability.

* If G,,(x) s 0, the undetermined coefficients of the third-order terms will all be zero and higher-order terms must be considered.