Instability of slowly varying systems
Instability criteria are obtained for systems described by \dot{x} = A(t)x when the parameters are slowly varying. In particular it is shown that, when A(t) has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then if \sup_{t \geq 0} \parallel \dot{A}...
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| Published in: | IEEE transactions on automatic control 1972-02, Vol.17 (1), p.86-92, Article 86 |
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| Main Authors: | , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Instability criteria are obtained for systems described by \dot{x} = A(t)x when the parameters are slowly varying. In particular it is shown that, when A(t) has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then if \sup_{t \geq 0} \parallel \dot{A}(t)\parallel is sufficiently small, the system has unbounded solutions. Results are also given for systems of the form \dot{x} = A(t)x + f(x, t) , and the dichotomy of solutions is studied in both the linear and nonlinear cases. |
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| ISSN: | 0018-9286 1558-2523 |