Global asymptotic stability of a class of nonlinear systems and networks
de Figueiredo, Rui J. P.
Master of Science
Stability results for a class of nonlinear systems which is composed of several nonlinear subsystems are obtained by means of Liapunov's direct method. The desired Liapunov function is constructed by a linear combination of the Liapunov functions for the subsystems. The stability condition is expressed in terms of the positive definiteness of some matrix. Stability results for a class of .nonlinear systems and networks which are described by vector Lurie type system equations are also obtained through an extension of Popov's theorem. Under the assumption that, with the nonlinear elements deleted, the system is asymptotically stable and nonlinear characteristic of each element is constrained to a sector, the steps in the proof of Popov's theorem are followed. The stability condition can be achieved by requiring some Hermitian matrix to be positive definite. The results are extended to the case where time delays are involved. Finally, a system of nonlinear networks interconnected by lossless transmission lines is considered. Here both time delay and loading effects are introduced. The stability results are derived in the same manner as above. Examples are included to illustrate the results.