In this paper, we propose the method for analyzing the nonlinear system in the time scale which is different from actual one. New time scale is defined as dt/dτ=s(x), where ‘t’ and ‘τ’ are actual time scale and that of defined one respectively, and s(x) is the function which we call ‘time scaling function’. Analysis of the system in new time scale ‘τ’ enables us to investigate the intrinsic structure of the system, in fact disturbance decoupling problem can be reviewed and extended in the sense of trajectory.
‘Wide-Sense Disturbance Decoupling Problem (WSDDP)’ is defined to seek feedback law and time scaling function which make the output transition in time scale ‘τ’ independent of disturbance, i.e. to seek feedback law which makes the output trajectory independent of disturbance. WSDDP is solved using new concepts ‘wide-sense (f, G) invariant distribution’ and ‘wide-sense locally (f, G) invariant distribution’.