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In this technical note we present a method for designing a linear time invariant (LTI) state-feedback controller to monotonically track a step reference at any desired rate of convergence for any initial condition. This method is developed for multi-input multi-output (MIMO) systems, and can be applied to strictly/nonstrictly proper systems, and also minimum/nonminimum-phase systems. This framework shows that for MIMO systems the objectives of achieving a rapid settling time, while at the same time avoiding overshoot/undershoot, are not always competing objectives. [ABSTRACT FROM AUTHOR]

This technical note introduces a new approach to the solution of a very general class of finite-horizon optimal control problems for discrete-time systems. This approach provides a parametric expression for the optimal control sequences, as well as the corresponding optimal state trajectories, by exploiting a new decomposition of the so-called extended symplectic pencil. This decomposition provides an original strategy for a more direct solution of the problem with no need of the system-theoretic hypotheses (including regularity of the symplectic pencil) that have always been assumed in the literature so far. [ABSTRACT FROM AUTHOR]

In this note it is shown that the main result of refid="ref1"/, concerning a characterization of a pair of structural invariant subspaces associated with the extended symplectic system, is a particular case of a result presented in refid="ref2"/ and refid="ref3"/ within a more general and rigorous context. We also analyse the proof of the main result of refid="ref1"/ , and the way such result is used to accomodate the boundary conditions in the solution of a finite-horizon linear quadratic optimal control problem. [ABSTRACT FROM PUBLISHER]