On controllability criteria for linear time-invariant singularly perturbed systems

For linear time-invariant singularly perturbed systems some effective necessary and sufficient conditions of complete controllability and controllability with respect to a part of variables are proved. All results are formulated in terms of defining equations that are matrix algebraic equations. These equations are constructed directly and are determined by a singularly perturbed system under investigation. A mathematical model of a moving passenger car with an active suspension as a control object for a singularly perturbed system is proposed. Results of the paper are applied to investigating complete controllability of an active suspension quarter-car model.