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The aim of this paper is to compare and discuss some old and new results on the discrete-time finite-horizon linear quadratic (LQ) optimal control problem in the case where the quadratic forms in the performance index are not assumed to be positive semidefinite, but only symmetric. We show in particular that the necessary and sufficient conditions presented in most contributions in the literature...
In this paper we analyze the properties of the set of solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. In particular, we study the relationship existing between the solutions of the generalized Riccati equation and the output-nulling subspaces of the underlying system. This analysis reveals the presence of a subspace that plays an important role in the...
In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency index of the closed-loop, from another part that...
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