| Abstract: | The concept of envelope system for a given dynamic system is proposed in this paper which refers to those systems whose module of transfer function in the whole range of frequency domain is always bigger than that of a given system. This concept opens a new way to study the problems of robust design and modelling for dynamic systems. The condition that an envelope system has to satisfy is rendered as the determination of the positiveness of a real polynomial function and Sturm's sequence method is used to establish an easily implemented criterion for evaluating the positiveness of the polynomial in terms of its coefficients. The optimization for the envelope system is expressed as the minimization of the 2-norm of its transfer function and simplex method is employed to search for the optimal solution. Two dynamic systems are used to illustrate the optimal design for the envelope systems of some of their responses. © 1998 John Wiley & Sons, Ltd. |
