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# H_∞ Norm and Control for Descriptor Symmetric Systems

Author: ZhangShanShan
Tutor: ZhangGuoShan
School: Tianjin University
Course: Control Theory and Control Engineering
Keywords: Generalized symmetric system Bounded real lemma H_ ∞ norm H_ ∞ control
CLC: TP11
Type: Master's thesis
Year: 2008
Downloads: 30
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### Abstract

 Symmetric systems are a class of systems with a special structure , has wide application background , the symmetric systems theory some progress has been made . In this paper, the current status quo of research on the theory of symmetric systems , further research more generally symmetrical system , generalized symmetric system H_ ∞ norm and generalized symmetric system H_ ∞ control problem . The main contents are as follows : ( 1 ) for the generalized symmetric system , two types of special circumstances symmetric system H_ ∞ norm calculation . By simple algebraic transformation , this problem is equivalent converted to corresponding normal symmetrical system , and with normal symmetrical system approach to solving . The H_ ∞ norm , more generally symmetrical system calculated the same time, this result is extended to the discrete time-invariant symmetric system . ( 2) study the generalized symmetric system H_ ∞ norm calculation . By using the generalized bounded real lemma the normal symmetric system results are extended to the generalized symmetric system . First, get two special cases of generalized bounded real lemma the solution , and then on this basis , and given the generalized symmetric system H_ ∞ norm expression . ( 3 ) study the generalized system status feedback, dynamic output feedback problem , given the presence of generalized system of the closed-loop system is symmetrical , allow the state feedback H_ ∞ controller and dynamic output feedback H_ ∞ controller , and further given the broad symmetric system dynamic the symmetrical output feedback H_ ∞ controller conditions .

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