This note introduces a new analytic approach to the solution of a verygeneral class of finite-horizon optimal control problems formulated fordiscrete-time systems. This approach provides a parametric expression for theoptimal control sequences, as well as the corresponding optimal statetrajectories, by exploiting a new decomposition of the so-called extendedsymplectic pencil. Importantly, the results established in this paper holdunder assumptions that are weaker than the ones considered in the literature sofar. Indeed, this approach does not require neither the regularity of thesymplectic pencil, nor the modulus controllability of the underlying system. Inthe development of the approach presented in this paper, several ancillaryresults of independent interest on generalised Riccati equations and on theeigenstructure of the extended symplectic pencil will also be presented.
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