2010
DOI: 10.1007/s11768-010-0039-2
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Infinite horizon LQR for systems with multiple delays in a single input channel

Abstract: This paper is concerned with the linear quadratic regulation (LQR) problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

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Cited by 7 publications
(15 citation statements)
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“…The system performance degradation or system instability could be arise from time delays. As for the estimation or control problems for the systems with time delay, there are several methods to settle such as the (partial difference) Riccati equation [35,36], the game-theoretic approach [37], the linear matrix inequality (LMI) method [38,39], and the convex optimization approach [40,41].…”
Section: Duality For Time-delay Systemsmentioning
confidence: 99%
“…The system performance degradation or system instability could be arise from time delays. As for the estimation or control problems for the systems with time delay, there are several methods to settle such as the (partial difference) Riccati equation [35,36], the game-theoretic approach [37], the linear matrix inequality (LMI) method [38,39], and the convex optimization approach [40,41].…”
Section: Duality For Time-delay Systemsmentioning
confidence: 99%
“…When multiple (different) delays enter into the system representation, neither the choice of the augmented state space, nor solvability conditions are immediately available [11]. Below, an augmented state space, extending the concepts established for single-delay systems, is introduced and its properties with respect to LQ optimal control problems are discussed.…”
Section: Problem Solution Via Augmented State Spacementioning
confidence: 99%
“…owing to decreased computational precision. However, in order to obtain a feasible solution in the infinitehorizon LQ problem it suffices to ensure stabilizability (reachability of all unstable modes) and detectability (mode observability by the cost function) [11], which are weaker than controllability and observability. Therefore, although easier to check in practice, controllability and observability should serve as a general indication if detectability and reachability are difficult to deduct.…”
Section: Remarkmentioning
confidence: 99%
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