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— Self-bounded controlled invariant subspaces play a key role in the synthesis of minimal-order dynamic regulators attaining model following by output feedback with stability. The approach, completely embedded in the geometric context, provides insight into the internal eigenstructure of the minimal self-bounded controlled invariant subspace, thus leading(More)
A new algorithmic setting is proposed for the discrete-time finite-horizon linear quadratic (LQ) optimal control problem with constrained or unconstrained final state, no matter whether the problem is cheap, singular, or regular. The proposed solution, based on matrix pseu-doinversion, is completed and made practically implementable by a nesting procedure(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 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 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)