New approach to asymptotic stability: time-varying nonlinear systems
The results of the paper concern a broad family of time-varying nonlinear systems with differentiable motions. The solutions are established in a form of the necessary and sufficient conditions for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system Ly...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117129700046X |
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| Summary: | The results of the paper concern a broad family of time-varying nonlinear systems with
differentiable motions. The solutions are established in a form of the necessary and sufficient conditions
for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system
Lyapunov function and 3) for an accurate single determination of the (uniform) asymptotic stability
domain. They permit arbitrary selection of a function p(⋅) from a defined functional family to
determine a Lyapunov function v(⋅), [v(⋅)], by solving v′(⋅)=−p(⋅) {or equivalently,
v′(⋅)=−p(⋅)[1−v(⋅)]}, respectively. Illstrative examples are worked out. |
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| ISSN: | 0161-1712 1687-0425 |