State space eigen value problem pdf

The state feedback eigenvalue placement problem is. 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. For distinct eigenvalues, the state transition matrix is given as. The only eigenvalues of a projection matrix are 0 and 1. Only issue is which set of states to use there are many choices.

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. In general, nonlinear differential equations are required to model actual dynamic systems. Statespace formulation for structural dynamics jose luis. What is the intuition of eigenvector and eigenvalue from a.

Explaining how the eigenvalues of the statespace a matrix relate to the poles of the transfer function. Eigenvalues and eigenvectors university of saskatchewan. In statedetermined systems, the state variables may always be taken as the outputs of integrator blocks. State space models dynamic behaviour of systems can be modeled by differential equations. So lets compute the eigenvector x 1 corresponding to eigenvalue 2. Eigen values are actually related to poles of the system. The behaviours of a state space system are governed by the eigenvalues of the a matrix. Infact each pole of system in transfer function form is eigen value of matrix a in state space form. The projection keeps the column space and destroys the nullspace. State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area. Weve reduced the problem of nding eigenvectors to a problem that we already know how to solve. Explaining how the eigenvalues of the state space a matrix relate to the poles of the transfer function. Assuming that we can nd the eigenvalues i, nding x i has been reduced to nding the nullspace na ii.