An algebraic approach to H∞ output feedback control problems

Sampei, Mitsuji; Mita, Tsutomu; Nakamichi, M.

doi:10.1016/0167-6911(90)90075-6

Cited by 160 publications

(31 citation statements)

References 2 publications

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“…The case that both the lower and the upper boundaries equal zero, i.e., L k = 0 = U k , means there does not exist any positive solution to inequality (13). We include it in the above discussion just for the completeness of the induction.…”

Section: Resultsmentioning

confidence: 94%

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On common solutions of Riccati inequalities

Sun

Yang

Peng

2011

J. Control Theory Appl.

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This paper extends the previous work on common positive definite solutions (CPDSs) to planar algebraic Riccati inequalities (ARIs) to those with arbitrary dimensions. The topological structure of the set of all positive definite solutions of an ARI is investigated. This leads to a necessary and sufficient condition for the existence of CPDSs to a set of Riccati inequalities. It also reveals that the solution set of ARIs is a positive cube in R n , which arouses a new method to search the CPDS. Some examples of three-dimensional ARIs are presented to show the effectiveness of the proposed methods. Unlike linear matrix inequality (LMI) method, the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.

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Section: Resultsmentioning

confidence: 94%

“…(13) Therefore, for the fixed t, x 1 , · · · , x k−1 , the positive solution x k to inequality (13) can be expressed as 0…”

Section: Resultsmentioning

confidence: 99%

On common solutions of Riccati inequalities

Sun

Yang

Peng

2011

J. Control Theory Appl.

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“…Finally, by the Schur complements, the LMI (18) [5] is that (18) is satisfied at all the prescribed points.…”

Section: Examplementioning

confidence: 99%

New results on linear parameter-varying time-delay systems

Mahmoud¹

2004

Journal of the Franklin Institute

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“…The regulator problem considered in H control theory is how to construct a controller that stabilizes the closed-loop system and minimizes the H norm of the closed-loop system transfer function [13]. The "rst objective of the H control design will be robust stabilization of the feedback control system against the unknown multiplicative perturbation.…”

Section: Control Objectivesmentioning

confidence: 99%