ZERO TIME ADJUSTMENT OF INITIAL CONDITIONS AND ITS RELATIONSHIP TO CONTROLLABILITY SUBSPACES

The ability to manipulate the release condition of the state vector from the input terminals of linear systems is of importance to a number of control applications. This problem has already received considerable attention for single-input single-output systems and suitable generalizations of the results to the multivariable case are discussed in this paper. A study of the geometric properties of the subspaces in the state space where the transferring of the state vector in minimum time is possible leads to the concept of controllability subspace in a manner that enables the unification of the existing physical, algebraic and geometric definitions of controllability subspace. A characterization of controllability subspace in terms of polynomial vectors is discussed together with possible applications for its computation. © 1974 Taylor & Francis Group, LLC.