Controllability of matrix second order systems: A trigonometric matrix approach

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.

Keywords

• Controllability
• matrix second order linear system
• cosine and sine matrices
• Banach contraction principle