EXISTENCE OF QUADRATIC TYPE LIAPUNOV FUNCTIONS FOR A CLASS OF NONLINEAR SYSTEMS

The contruction of Liapunov functions is presented non-linear systems related to the Lur'e problem. The method presented consists in developing a quadratic type Liapunov functioncalled a spanning Liapunov function (SLF)-for an associated linear system, and modifying it suitably for the nonlinear case. Using this approach, a theorem of Popov, for the Lur'e problem is derived and is extended to the case with m nonlinearities. Condition for the existence of a Liapunov function of this form for the case of a gain in the Lur'e problem are derived. The results are used to construct Liapunov functions for certain specific systems. (Author) Unclassified report