Dual lattices for non-strictly proper systems

Abstract

This paper investigates the dual lattice structures of self-bounded and self-hidden subspaces of linear time-invariant systems arising in the solution of disturbance decoupling, regulator and unknown-input observation problems. The case that we are addressing in this paper is the one where the algebraic feedthrough matrices are allowed to be nonzero. We show that, in this general case, the additional constraints that need to be taken into account for the solution of the aforementioned control/estimation problems are no longer simple subspace inclusions as in the strictly proper case. As a consequence, mathematical apparatus underpinning the structure of the dual lattices of self bounded and self hidden subspaces in this more general framework becomes more challenging and richer.