Efficient Stability and Robustness Analysis of Uncertain Nonlinear Systems Using Simulation Data  
Author Young Kap Son


Co-Author(s) Gordon J. Savage


Abstract The stability of dynamic systems is important for safety, reliability and satisfactory performance. The study becomes more difficult when the system is nonlinear and when the ever present uncertainties in the components must be considered. Herein a new approach is presented to determine the stability space of nonlinear, uncertain dynamic systems: the method is very simple and obviates the traditional eigenvalue approach and the accompanying linearizing approximations. Herein time-domain information is used in an economical way as follows: i) the design space is overlain by an array of grid points of suitable spacing, ii) design of experiments helps capture the variability of the design variables about a particular grid point, iii) corresponding computer simulations of the actual system, over only a small period of time, generate a matrix of discrete time responses, and finally, iv) singular value decomposition separates out parameter and time information. The variability of the first few left and right singular vectors predicts any instability that might occur over the timespan of the dynamics. The method can be implemented with readily available software routines. A study of a practical engineering system with different tolerances shows the efficacy of the proposed approach.


Keywords Dynamic systems, Nonlinear, Uncertain, Robustness, Stability, Singular Value Decomposition
    Article #:  22269
Proceedings of the 22nd ISSAT International Conference on Reliability and Quality in Design
August 4-6, 2016 - Los Angeles, California, U.S.A.