✦ LIBER ✦

Sensitivity analysis of the discrete-time algebraic Riccati equation

✍ Scribed by Ji-guang Sun

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 958 KB
Volume: 275-276
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10017-9

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✦ Synopsis

Consider the discrete-time algebraic Riccati equation (DARE) ATXA -X -(ATXB + S)(R + B?fB)~' (F/U + ST) + Q = 0,

where A E W"", B, S t (w"""'~ R = RT E LQ"""' , Q = QT E W"'. The available perturbation theory for the DARE can only be applied to the case R > 0. However, in some control problems the matrix R can be singular. In this paper we study perturbation properties of the DARE without the restriction R > 0. Perturbation bounds and a relative condition number for the stabilizing solution of the DARE are derived. Computable residual bounds for an approximate solution are also derived. The theoretical results are illustrated by numerical examples.

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