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- W1202125262 abstract "In this work the Second Method of Liapunov is used in conjunction with the Poincare-Bendlxson Theorem to ex amine methods of determining or specifying limit cycles in J second and third order systems. For second order systems the variable gradient method is used to find contact curves in the construction of the annular region required by the Poincare-Bendlxson Theorem. In this manner it is possible to bound the limit cycle to a region of the state plane. With regard to finding the exact limit cycle a method is formulated by defining a Liapunov function referred di rectly to the limit cycle. Since the limit cycle is unknown a priori. the Liapunov function is defined as a known function of an unspecified closed curve. The form of the Liapunov function is chosen according to the geometrical requirements of the Poincare-Bendixson Theorem. Thus, for the two dimen sional case, the Liapunov function represents two concentric closed curves and, in three dimensions, a toroid. Making use of the hypothesis of the Poincare-Bendlxson Theorem that all the trajectories cross the region bounding the limit cycle in an inward direction, the time derivative of the Liapunov function is forced to be negative definite with respect to" @default.
- W1202125262 created "2016-06-24" @default.
- W1202125262 creator A5077332735 @default.
- W1202125262 date "1965-01-01" @default.
- W1202125262 modified "2023-10-13" @default.
- W1202125262 title "On the construction of Liapunov functions for third order control systems with limit cycles" @default.
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