Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 80, pp. 1-14.

Title: Controllability of matrix second order systems:
       A trigonometric matrix approach

Authors: Jaita Pankaj Sharma (Univ. of Baroda, Vadodara, India)
         Raju K. George      (Univ. of Baroda, Vadodara, India)

Abstract:
 Many of the real life problems are modelled as Matrix Second Order
 Systems, (refer Wu and Duan [19], Hughes and
 Skelton [10]). Necessary and sufficient condition for
 controllability of Matrix Second Order Linear (MSOL) Systems has
 been established by Hughes and Skelton [10]. However, no
 scheme for computation of control was proposed. In this paper we
 first obtain another necessary and sufficient condition for the
 controllability of MSOL and provide a computational algorithm for
 the actual computation of steering control. We also consider a
 class of  Matrix Second Order Nonlinear systems (MSON) and provide
 sufficient conditions for its controllability. In our analysis we
 make use of Sine and Cosine matrices and employ Pade
 approximation for the computation of matrix Sine and Cosine. We
 also invoke tools of nonlinear analysis like fixed point theorem
 to obtain controllability result for the nonlinear system. We
 provide numerical example to substantiate our results.
  
Submitted February 15, 2007. Published May 29, 2007.
Math Subject Classifications: 93B05, 93C10.
Key Words: Controllability; matrix second order linear system;
           cosine and sine matrices; Banach contraction principle.