時間軸の変換を用いた非線形システムの線形化

新時間軸での線形化

抄録

In this paper, we are concerned with the linearization in a new time scale‘τ’, which is defined as dt/dτ=s(x). It is shown that there exist nonlinear systems which cannot be linearized in the ordinary time scale ‘t’ but can be linearized in a new time scale ‘τ’. Because the new time scale ‘τ’ does not go backward against the actual time ‘t’, controllers which stabilize the system written in the new time scale ‘τ’ also stabilize the actual system. So it is meaningful, in the sense of stability, to be concerned with the linearization in the new time scale.
We define ‘wide-sense feedback equivalence’ in order to study the linearization in some time scale, and derive the conditions for the system to be wide-sense feedback equivalent to a linear system. In this case, time scaling function which make system linear is derived as the solution of the differential equations.