Liapunov functions derived from auxiliary exact differential equations

✍ Scribed by Edwin Kinnen; Chiou-Shiun Chen

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 497 KB
• Volume: 4
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(68)90014-9

✦ Synopsis

The intuitive and experience based methods that have characterized the deveioprnent of Liapunov functions are re-examined. Attention is redirected from finding terms of a scalar function or a gradient to components of a vector h. While practical advantages of this perspective would depend on the background of the analyst, it is shown that genre'ally less freedom results when arbitrary forms for either V, ~'or VVare initially selected. This is signiticant when unfamiliar nonlinear ditfcr~tial equations are under investigation. The introduction of the vector h creating an auxiliary exact differential equation also provides a unity to the disparate methods that have been proposed by many writers ever since Liapunov's work was originally published. And as a consequence, a conceptual base is established from which new prooe, dures may more readily evolve.