Single Diophantine equation solution of the discrete-time polynomial H2 and H∞ control problems with a classical feedback structure

Haipeng Zhao; Joseph Bentsman

Single Diophantine equation solution of the discrete-time polynomial H₂ and H_∞ control problems with a classical feedback structure

Research output: Contribution to journal › Article › peer-review

Abstract

The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H₂ and H_∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H_∞ control problem.

Original language	English (US)
Pages (from-to)	676-681
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
State	Published - 2001
Externally published	Yes

ASJC Scopus subject areas

Chemical Health and Safety
Control and Systems Engineering
Safety, Risk, Reliability and Quality

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AB - The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H2 and H∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H∞ control problem.

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Single Diophantine equation solution of the discrete-time polynomial H2 and H∞ control problems with a classical feedback structure

Abstract

ASJC Scopus subject areas

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Single Diophantine equation solution of the discrete-time polynomial H₂ and H_∞ control problems with a classical feedback structure