So lets compute the eigenvector x 1 corresponding to eigenvalue 2. Assuming that we can nd the eigenvalues i, nding x i has been reduced to nding the nullspace na ii. Eigenvalues and eigenvectors university of saskatchewan. This, of course, will be determined in part by the choice of k. The state feedback eigenvalue placement problem is. Infact each pole of system in transfer function form is eigen value of matrix a in state space form. Eigen values are actually related to poles of the system. Statespace formulation for structural dynamics jose luis. In general, nonlinear differential equations are required to model actual dynamic systems.
In many cases, however, linear approximations can be obtained to describe the dynamic behaviour. The only eigenvalues of a projection matrix are 0 and 1. The problem is that for the state space formulation the system matrix is nonsymmetric and therefore its eigenvalues and eigenvectors are complex which require further understanding of complex formulation. The eigenvalues and eigenvectors which result from the state space eigenvalue problem will contain the same information as in the second order eigenvalue problem, but will be in a different form. For distinct eigenvalues, the state transition matrix is given as. The behaviours of a state space system are governed by the eigenvalues of the a matrix. Explaining how the eigenvalues of the state space a matrix relate to the poles of the transfer function. This result follows directly from a laplace transform analysis and also from a similarity transform using the eigenvectors. Weve reduced the problem of nding eigenvectors to a problem that we already know how to solve. What is the intuition of eigenvector and eigenvalue from a. State space models dynamic behaviour of systems can be modeled by differential equations.