Arbitrary eigenvalue assignments for linear time-varying multivariable control systems

The problem of eigenvalue assignments for a class of linear time-varying multi-variable systems is considered. Using matrix operators and canonical transformations, it is shown that a time-varying system that is ‘lexicography-fixedly controllable’ can be made via state feedback to be equivalent to a time-invariant system whose eigenvalues are arbitrarily assignable. A simple algorithm for the design of the state feedback is provided.