Novel Canonical Forms for Linear Time-Varying Multivariable Systems and their Applications

The controller and observer block-bidiagonal-Frobenius forms for a class of linear time-varying multivariable systems are presented, respectively. These can be employed in the state-feedback pole-placement and state-observer designs such that the closed-loop system is time-invariant, with the advantage that these do not need to compute the characteristic matrix polynomial coefficients as required when using the block canonical forms. The feedback gain matrices are given directly from the block-bidiagonal-Frobenius forms without any computation.