Comparative study on the computation of state transition matrix using La-grange's interpolation technique and Cayley-Hamilton theorem

Abstract

The state transition matrix (STM) can be used to obtain the general solution of linear dynamical systems in electrical engineering. For any control system, to understand its behaviour and properties, calculating the STM is very crucial. There are several ways to calculate STM out of which we usually use the Cayley-Hamilton theorem or Laplace transform method. This paper presents the comparative study of the computation of state transition matrix using La-grange's Interpolation formula and Cayley-Hamilton theorem. In addition, this paper also suggests how to find the controllability matrix using the La-grange's Interpolation formula during the design of the pole-placement design approach. This method can be included in the academic book to study the course on state space analysis.