A lyapunov function with applications to some nonlinear physical systems

✍ Scribed by H.H. Rosenbrock

• Publisher: Elsevier Science
• Year: 1963
• Tongue: English
• Weight: 920 KB
• Volume: 1
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(63)90005-0

✦ Synopsis

The paper gives a Lyapunov function which can be used for certain naturallyoccurring systems of nonlinear simultaneous differential equations. The equations arise when there is a flow of some physical quantity such as heat, matter or electricity through an appropriate physical system.

The Lyapunov function can be used to examine the stability of such systems. It can also be used to give a criterion for automatic control. Brief applications are given to distillation columns and heat exchangers.

Mathematical results are obtained for systems which give rise to sets of ordinary differential equations. Continuous systems, which are usually described by partial differential equations, are dealt with by the use of discontinuous physical models.

J

FIo. 1. System of stirred tanks. * Subject to the condition mentioned in the previous footnote.