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arXiv · 1305.5311

A reduction technique for Generalised Riccati Difference Equations

Augusto Ferrante·Lorenzo Ntogramatzidis
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Abstract

This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In particular, an analysis on the eigen- structure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalised discrete algebraic Riccati equation are coin- cident. This subspace is the key to derive a decomposition technique for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of steps equal to the nilpotency index of the closed-loop, from another part that can be computed by iterating a reduced-order generalised Riccati difference equation.

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Augusto Ferrante, Lorenzo Ntogramatzidis. 2013-05-23. A reduction technique for Generalised Riccati Difference Equations. https://arxiv.org/abs/1305.5311

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