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The problem of the non-causal inversion of linear multivariable discrete-time systems is analyzed in the geometric approach framework and is solved through the computation of convolution proÿles which guarantee perfect tracking under the assumption of inÿnite-length preaction and postaction time intervals. It is shown how the shape of the convolution… (More)

—The Hamiltonian system related to discrete-time cheap linear quadratic Riccati (LQR) problems is analyzed in a purely geometric context , with the twofold purpose of getting a useful insight into its structural features and deriving a numerically implementable solution for the infinite horizon case by only using the standard geometric approach routines… (More)

The purpose of this paper is to derive constructive necessary and sufficient conditions for the problem of disturbance decoupling with algebraic output feedback. Necessary and sufficient conditions have also been derived for the same problem with internal stability. The same conditions have also been expressed by the use of invariant zeros. The main tool… (More)

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the… (More)

The problem of making the output insensitive to an exogenous input signal possibly known with preview is tackled in the geometric approach context. The definition of minimal preview for decoupling is introduced. Necessary and sufficient constructive conditions for decoupling with minimal preview are proved by means of simple geometric arguments. The… (More)