Quantitative Design of Mimo Nonlinear Uncertain Feedback Systems Having Nonzero Initial Conditions

An n × n nonlinear uncertain multiple-input multiple-output plant W, known only to belong to a set {W} is considered. At t=0 it is transformed into a one-degree-of-freedom feedback structure with compensation G. A synthesis method is developed to design G so that a given level of attenuation of plant output is attained for all Wε{W} and for any set of initial conditions y0ε{y0} on output of the plant W. The design philosophy is to convert the problem into a disturbance attenuation problem for uncertain linear time invariant systems with zero initial state, which in turn is converted into a series of successive single-input-output problems of the disturbance attenuation type. A design example is included.