Approximate input-output linearization of nonlinear systems

Abstract

We will define an approximate input-output linearization problem -- an order ? input-output linearization problem. To solve this, we must find a feedback u=?(x)+s(x)v for the system x=f(x)+g(x)u, y =h(x) such that the input-output response will be order ? input-output linear, i.e. its Volterra series expansion (V.S.E.) will be y(t) = W0(t) + ?i=1 m ?0 t{?p=0 ?K(i,p)(t-?)p/p!}vi(?)d? +?j=1 ?W(?+j) where W(k) is k-th order term of V.S.E. This system will be approximately linear if the kernels of order larger than ? are negligible. We will identify, using a modified structure algorithm, the class of nonlinear systems which can be transformed into order ? input-output linear systems. We will also show that, under suitable conditions, an order ? input-output linear system can be expressed in an appropriate state as ? = F? + Gv +od(?, ?, v)?+1 ? = f?(?, ?) + ?(?, ?)v y = H? where F, G and H are matrices of real numbers.