A derivation of the Glover-Doyle algorithms for general H∞ control problems

Hong, Jia‐Sheng; Teng, Ching‐Cheng

doi:10.1016/0005-1098(95)00117-4

Cited by 14 publications

(15 citation statements)

References 15 publications

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“…This is shown in Figure 6. The reason for K to be an internally stabilizing controller is similar to the proof given in [9] or [17] and is omitted. However, by the Youla parameterization, because (equation (15)) is outer, a family of the internally stabilizing controller K can be chosen as…”

Section: (B) If the Conditions Of Part (A) Are Satisfied Then All Ofmentioning

confidence: 96%

“…Motivated by the combination of (J, J )-lossless systems with the CSMD approach to linear or nonlinear H ∞ control ( [9], [10], [16], [24]), one is now concerned with constructing discrete-time state-delayed systems that are (J, J )-lossless or conjugate (−J, −J )-lossless.…”

Section: The Csmd and (J J )-Lossless Systemsmentioning

confidence: 99%

“…This implies that the output energy is less than or equal to the input energy, which leads to the following interesting result ( [9], [16], and [24]). Then || || ∞ < 1 ⇒ ||F R ( , )|| ∞ < 1 (i.e., ||z|| 2 2 < ||w|| 2 2 or ||u|| 2 2 − ||y|| 2 2 ≥ ||z|| 2 2 − ||w|| 2 2 ).…”

Section: And Then the Preceding Equation Is Equal Tomentioning

confidence: 99%

“…In the present study, we aim to extend the chain-scattering matrix description approach (see e.g., [1], [6], [9], [16], [17], [24]) to the H ∞ state-delayed control problem, because this kind of approach can be described by block diagrams, which always make the solving process brief. It is shown that, while the discrete-time state-delayed systems are stabilizable and detectable, there always exist right-and left-coprime factorization with each coprime factor possessing the same delayed states as that of the original system.…”

Section: Introductionmentioning

confidence: 99%

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An H? Output Feedback Control for Discrete-Time State-Delayed Systems

Hong

2004

Circuits Syst Signal Process

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A coprime factorization approach to H ∞ controller design for discrete-time state-delayed systems is developed. The coprime factors that are generated by the present factorization possess the same delayed state as that of the original system. This property, together with the well-known Youla parameterization and the chain-scattering matrix setting, provides a relatively simple method for obtaining a family of internally stabilizing H ∞ output feedback controllers. A numerical example is given to demonstrate the validity and applicability of the proposed approach.

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Section: (B) If the Conditions Of Part (A) Are Satisfied Then All Ofmentioning

confidence: 96%

Section: The Csmd and (J J )-Lossless Systemsmentioning

confidence: 99%

Section: And Then the Preceding Equation Is Equal Tomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An H? Output Feedback Control for Discrete-Time State-Delayed Systems

Hong

2004

Circuits Syst Signal Process

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“…Also, Kimura [5] and Ball et al [6] developed a "ctitious signals method to solve the linear 4-block control problem. Hong and Teng [7] then developed a new method which both matched the famous results of Glover et al [2] and removed the "ctitious signals.…”

Section: Introductionmentioning

confidence: 98%

H^∞ control for nonlinear affine systems: a chain‐scattering matrix description approach

Hong

Teng

2001

Intl J Robust & Nonlinear

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SUMMARYThis paper combines an alternative chain-scattering matrix description with (J, J)-lossless and a class of conjugate (!J, !J)-lossless systems to design a family of nonlinear H output feedback controllers. The present systems introduce a new chain-scattering setting, which not only o!ers a clearer expression for the solving process of the nonlinear H control problem but also removes the "ctitious signals introduced by the traditional chain-scattering approach. The intricate nonlinear a$ne control problem thus can be transformed into a simple lossless network and is easy to deal with in a network-theory context. The relationship among these (J, J) systems,¸-gain, and Hamilton}Jacobi equations is also given. Block diagrams are used to illustrate the central theme.

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