More on the controllability of linear time-invariant systems

Abstract

This study shows that a controllable system [xdot] = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x0 to an arbitrary final condition x(tf = xf by a polynomial control function of degree M = 2r + 1, where r = n − rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.