Existence and computation of linear state-transformations into the controllability/observability canonical forms of large-scale nonlinear systems

By circumventing symbolic Lie algebraic computations, sensitivity-based algorithms very efficiently compute controllability/observability of large-scale nonlinear dynamical systems. Also, they provide controllability/observability signatures, pinpointing the state variables involved in uncontrollable/unobservable modes. One contribution of this paper is to show that these algorithms can also be used to determine whether the transformation into the controllability/observability canonical form is linear or not. If linear, this paper also reveals how this transformation is obtained from the sensitivity-based algorithm. Another contribution is to show that this linear transformation can also be obtained from standard algorithms, putting linear time-invariant systems into the controllability/observability canonical form. Examples of medium- and large-scale nonlinear dynamical systems are presented to illustrate these contributions.