ON THE INVERSION OF CERTAIN NONLINEAR-SYSTEMS

In this letter, we present some theorems for the exact inversion and t he pth-order inversion of a wide class of causal, discrete-time, nonli near systems, The nonlinear systems we consider are described by the i nput-output relationship y(n) = g[x(n)]h[x(n-1). y(n-1)]+f[x(n-1), y(n -1)], where 9[.], h[..], and f[..] are causal, discrete-time and nonli near operators and the inverse function g(-1)[.] exists. The exact inv erse of such systems is given by z(n)] = g(-1)[{u(n)-f[z(n-1). u(n-1)] }/h[z(n-1), u(n-1]]. Similarly, when h[..]=1, the pth-order inverse is given by z(n)=g(p)(-1)[u(n)-f[z(n-1). u(n-1)]] where g(p)(-1) [.] is the pth-order inverse of g[.].