(J, J?)-Spectral factorization and conjugation for discrete-time descriptor system

The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.

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A -spectral factorization approach for H∞ estimation problems in discrete time

IEEE Transactions on Automatic Control ◽

10.1109/tac.2002.805666 ◽

2002 ◽

Vol 47 (12) ◽

pp. 2108-2113 ◽

Cited By ~ 24

Author(s):

P. Colaneri ◽

A. Ferrante

Keyword(s):

Discrete Time ◽

Spectral Factorization ◽

Factorization Approach ◽

Estimation Problems

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A Descriptor System Approach to Stability and Stabilization of Discrete-Time Switched PWA Systems

IEEE Transactions on Automatic Control ◽

10.1109/tac.2018.2797173 ◽

2018 ◽

Vol 63 (10) ◽

pp. 3456-3463 ◽

Cited By ~ 66

Author(s):

Yanzheng Zhu ◽

Zhixiong Zhong ◽

Michael V. Basin ◽

Donghua Zhou

Keyword(s):

Discrete Time ◽

System Approach ◽

Descriptor System ◽

Stability And Stabilization

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A Simplified Descriptor System Approach to Delay-Dependent Stability and Robust Performance Analysis for Discrete-Time Systems with Time Delays

Mathematical Problems in Engineering ◽

10.1155/2013/810271 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Fengying Xu ◽

Daxin Li

Keyword(s):

Performance Analysis ◽

Discrete Time ◽

System Approach ◽

Descriptor System ◽

Linear Matrix ◽

Quadratic Cost ◽

Discrete Time Systems ◽

Delay Dependent ◽

Time Systems ◽

Delay Dependent Stability

A simplified descriptor system approach is proposed for discrete-time systems with delays in terms of linear matrix inequalities. In comparison with the results obtained by combining the descriptor system approach with recently developed bounding technique, our approach can remove the redundant matrix variables while not reducing the conservatism. It is shown that the bounding technique is unnecessary in the derivation of our results. Via the proposed method, delay-dependent results on quadratic cost andH∞performance analysis are also presented.

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