The structure of decoupled non linear systems

Decoupling of linear time-invariant systems by state feedback and precompensation has been treated in several papers (Falb and Wolovich 1967, Gilbert 1969, Wonham and Morse 1970, Silverman and Payne 1(71). A generalization of some results for time-variable systems was given by Porter (1969) and Freund (1971 a, b). Decoupling of non-linear time-variable systems by state feedback was considered by Porter (1970) where a feedback law as a sufficient condition for decoupling was presented. In this paper the results of Porter (1970) on decoupling are extended for the case D(x, t),., 0 and a more general feedback law is derived. This feedback law permits an arbitrary assignment of a specified number of poles and is a generalization of the synthesis procedure of Falb and Wolovich (1967) for the non-linear time-variable case. In the subsequent section the structure of the decoupled closed-loop system with respect to observability is considered. This type of problem has been regarded for linear systems with constant coefficients by Mufti (1969). For this purpose a sufficient criterion for observability of non-linear timevariable systems is introduced and applied to the closed-loop decoupled system with arbitrary pole assignment. The analysis based on this criterion leads to results about the structure of the decoupled system and to a sufficient condition.... for the observability of the decoupled non-linear time-variable system.