Further result on performance degradation for nonlinear multivariable systems

Kouvaritakis, Harrison, and Latchman (1987) derived bounds on the worst-case deviation that the response of a nonlinear multivariable system can make from its nominal (linear) response. The technique presented there makes use of the properties of L₂ norms of truncated functions and recently developed matrix scaling techniques to reduce the conservativism which derives from the multivariable nature of the problem. The result thus obtained may be computed for any time point and provides time-dependent bounds on the system response functions. The current paper presents a refinement of the earlier method and shows, by means of an example, that the new bounds can be significantly less conservative during the transients, than those proposed in the earlier paper.