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In this paper we present a method for designing a linear time invariant (LTI) state-feedback controller to monotonically track a constant step reference at any desired rate of convergence for any initial condition. This framework shows that for MIMO LTI systems the objectives of achieving a rapid settling time, while at the same time avoiding overshoot and/or undershoot, are not necessarily competing...
A geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem and the output-nulling and reachability subspaces of the underlying system. This analysis reveals the presence of a subspace that plays a crucial role in the solution of the related optimal control...
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