Regions of asymptotic stability for distributed parameter systems

✍ Scribed by C.R. McGowin; D.D. Perlmutter

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 776 KB
• Volume: 26
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(71)83002-6

✦ Synopsis

Liapunov-collocation technique is proposed for the analysis of regions of asymptotic stability (RAS) in distributed parameter systems whose unsteady state behavior is described by a system of parabolic partial differential equations. First, the collocation method is used to reduce the partial differential equations to an approximately equivalent set of ordinary differential equations. Second, Liapunov's Direct Method is used to estimate the RAS in collocation space. Finally, points from the boundary of the Liapunov RAS are mapped into profile space to yield the RAS boundary profiles.

The technique was used to obtain regions of asymptotic stability for the catalyst particle with slab geometry. The method generated RAS boundaries in profile space that reflected the effects of profile shape and the relative signs of concentration and temperature disturbances.