THE ANALYSIS OF A CERTAIN CLASS OF NONLINEAR SYSTEMS,
Abstract
In nonlinear analysis, the partitioning technique has been used to analyze a certain class of non linear systems whose dynamic behavior can be rep resented by a nonlinear differential equation with time-varying parameters. When suitable re strictions were placed on the linear, nonlinear, and forcing function terms, the system equation presented a unique solution which existed to the right of the initial state. The system solution was given as a limit of a sequence of Picard iterates X sub n which are well defined in a given domain and which belong to L sub 2 space. A for mula was developed which permits determining the number of iterates necessary for the approxima tion of the solution in the mean square sense. Within the restrictions imposed on the system, the system response was found to be uniformly con tinuous with resp the initial conditions and the system parameters. Two different defini tions of the norms were selected, and the behavior of the system trajectory was investigated for two important cases: (1) at any instant of time and (2) on the average during an interval of interest. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1963
- Accession Number
- AD0418193
Entities
People
- A.y. Bilal
Organizations
- University of Michigan