Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems

✍ Scribed by W.F. Trench

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 622 KB
• Volume: 36
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(98)80027-8

✦ Synopsis

Following an idea originated by Conti for continuous matrix functions, an equivalence relation called summable similaritt/ is defined on pairs of n x n matrix functions A and B. Special cases of the results show that if A and B are summably similar and the system {A} &em =Am:!:m, m =0, 1, 2, . .. is uniformly, exponentially, or strictly stable, or has linear asymptotic equilibrium, then the system {B} ~t/m =Bmt/m, m =0, 1,2, ... has the same property. More generally, the same conclusion is obtained under weaker conditions relating A and B.