Existence and computation of linear state-transformations into the controllability and observability canonical form of nonlinear dynamical systems

Abstract Sensitivity-based algorithms very efficiently compute controllability/observability of large-scale linear and 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 of nonlinear dynamical systems 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.