Superstability of linear switched systems. (English) Zbl 1317.93125
Summary: This paper applies the concept of superstability to switched linear systems as a particular case of linear time-varying systems. A generalised concept of superstability, applied to complex matrices, and extended superstability, is introduced in order to obtain a new result for guaranteeing the asymptotic stability of a switched system under arbitrary switching. The relation between extended superstable and stable simultaneously triangularizable sets of matrices is also discussed. It is shown that stable triangularizable matrices are a proper subset of extended superstable ones, pointing out that the presented stability result is a generalisation of the previous well-known stability theorems to a broader class of switched dynamical systems.
MSC:
| 93C05 | Linear systems in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 34D99 | Stability theory for ordinary differential equations |
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