DocumentCode :
1658214
Title :
A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback
Author :
Bin, Zhou ; Guangren, Duan ; Zongli, Lin
Author_Institution :
Harbin Inst. of Technol., Harbin
fYear :
2007
Firstpage :
678
Lastpage :
682
Abstract :
Low gain feedback has found several applications in constrained control systems, robust control and nonlinear control. Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic Riccati equation (ARE). The eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter, while the ARE approach requires the solution of an ARE for each value of the parameter. This paper proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov equation. Such an approach possesses the advantages of both the eigenstructure assignment approach and the ARE based approach. It also avoids the possible numerical stiffness in solving a parametric ARE and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach.
Keywords :
Lyapunov matrix equations; Riccati equations; eigenvalues and eigenfunctions; nonlinear control systems; polynomial matrices; robust control; state feedback; constrained control systems; eigenstructure assignment algorithm; low gain feedback; matrix polynomial; nonlinear control; parametric Lyapunov equation approach; parametric algebraic Riccati equation; robust control; stabilizing state feedback gains; Control systems; Hydraulic actuators; Hydrogen; Linear systems; Nonlinear control systems; Performance gain; Poles and zeros; Polynomials; Riccati equations; State feedback; actuator saturation; global stabilization; low gain feedback; parametric Lyapunov equation; semi-global stabilization; set invariance;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Conference, 2007. CCC 2007. Chinese
Conference_Location :
Hunan
Print_ISBN :
978-7-81124-055-9
Electronic_ISBN :
978-7-900719-22-5
Type :
conf
DOI :
10.1109/CHICC.2006.4347632
Filename :
4347632
Link To Document :
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