Observability canonical (phase-variable) form for non-linear time-variable systems

Abstract

An observability canonical form for non-linear time-variable systems, [xdot]=f(x,u,t), y=h(x,u,t), is introduced by analogy with the corresponding linear phase-variable forms. The transformation into observability canonical form follows from the nonlinear observability map, whose jacobian must be assumed to be a regular matrix in the considered domains of state x, input u and time t. If this observability matrix can be inverted analytically or numerically, the transformation into the observability canonical coordinates can be achieved directly. As opposed to linear systems, the non-linear observability canonical form with input depends, additionally, on the time derivatives of the input. This restricts a practical implementation.