An orthogonal method for the controllable subspace of a periodic system
J. Sreedhar, Paul Van Dooren · 1993
We describe a method for computing the controllable subspace of a linear periodic discrete time system. The method is based on the ordered periodic Schur form [1] of a matrix sequence A i ; i = 0; : : : ; K \\Gamma1, and proceeds by reducing the state equation to a convenient form in which the controllable/uncontrollable states are clearly displayed. Its attractive features are simplicity, numerical accuracy and stability. 1. Introduction A basic problem connected with linear systems is to compute the controllable subspace. Consider the following discrete-time system x k+1 = A k x k +B k u k ; (1) where A k 2 C n\\Thetan , B k 2 C n\\Thetam are known periodic matrices of integer period K, i.e., A k+K = A k ; B k+K = B k ; 8 k 2 Z; and x k , u k are vectors of states and inputs respectively. For the special case of time-invariant systems (period K = 1), this problem has been studied extensively, beginning with the work of Kalman -- see for instance [2], [3], [4], [5]. We know tha...