Linearization of Nonlinear Systems

Work accomplished Low crest-factor signals A detailed study of the the problem of low crest-factor signals is made based on the techniques used in harmonic probing of nonlinear systems. Particularly interesting here is the numerical evidence suggesting that the phases used originally exceed the performance achievable with the Shapiro-Rudin phases, which can be proved to yield bounded crest factor for multitone signals containing an arbitrarily large number of tones. Bounding and computing gains of systems The crest factor problem relates two norms, L-sq and L at infinity, of a signal comparing the gains of an operator with respect to two norms is much harder. Numerical determination of Performance limits A new computational method for the design of linear controllers was developed. and Computational stability analysis A new method of computational stability analysis of systems is derived. Many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of x-dot Ax for some appropriate A. The existence of such a Lyapunov function can be determined by solving a nondifferentiable convex program.