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On semi-global stabilization of minimum phase nonlinear systems without vector relative degrees

Science in China(Series F) 2009年第11期52卷 2153-2162页

作者： LIU XinMin LIN ZongLi Charles L. Brown Department of Electrical and Computer Engineering University of Virginia P.O. Box 400473 Charlottesville VA 22904-4743 USA

Recently, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. This structural decomposition simplifies the conventional backstepping design and allows a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable. In this paper we further exploit the properties of such a decomposition for the purpose of solving the semi-global stabilization problem for minimum phase nonlinear systems without vector relative degrees. By taking advantage of special structure of the decomposed system, we first apply the low gain design to the part of system that possesses a linear dynamics. The low gain design results in an augmented zero dynamics that is locally stable at the origin with a domain of attraction that can be made arbitrarily large by lowering the gain. With this augmented zero dynamics, backstepping design is then applied to achieve semi-global stabilization of the overall system.

关键词： nonlinear systems structural decomposition semi-global stabilization low gain feedback

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stabilization of Linear Systems with Distributed Delay and Saturation Nonlinearity

Stabilization of Linear Systems with Distributed Delay and S...

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第三十届中国控制会议

作者： ZHOU Bin~1,GAO Huijun~2,LIN Zongli~3,DUAN Guang-Ren~1 1.Center for Control Theory and Guidance Technology,Harbin Institute of Technology,P.R.China. 2.Space Control and Inertial Technology Research Center,Harbin Institute of Technology,P.R.China. 3.Charles L.Brown Department of Electrical and Computer Engineering,University of Virginia,U.S.A.

＜正＞This paper is concerned with stabilization of a linear system with distributed input delay and input *** constant and time-varying delays are *** the case that the input delay is constant,under the stabilizability assumption on an auxiliary system,it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open-loop system is not exponentially *** the case that the input delay is time-varying,but bounded,it is shown that the system can be stabilized by state feedback if the non-asymptotically stable poles of the open-loop system are all located at the *** both cases,stabilizing controllers are explicitly constructed by utilizing the parametric Lyapunov equation based low gain design approach we recently *** is also shown that in the presence of actuator saturation and under the same assumptions on the system,these controllers achieve semi-global *** discussions on the assumptions we impose on the system are given.A numerical example illustrate the effectiveness of the proposed stabilization approach.

关键词： Distributed input delay Input saturation Parametric Lyapunov equation stabilization semi-global stabilization

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A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback

A Parametric Lyapunov Equation Approach to the Design of Low...

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第二十六届中国控制会议

作者： Zhou Bin1,Duan Guangren1,Lin Zongli2 1.Center for Control Theory and Guidance Technology,Harbin Institute of Technology,P.O.Box 416,Harbin,Heilongjiang 150001,P.R.China2.Charles L.Brown Department of Electrical and Computer Engineering,University of Virginia,P.O.Box 400743,Charlottesville,VA22904-4743,U.S.A.

Low gain feedback has found several applications in constrained control systems,robust control and nonlinear *** 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 *** 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 *** paper proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov *** an approach possesses the advantages of both the eigenstructure assignment approach and the ARE based *** 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.

关键词： low gain feedback actuator saturation semi-global stabilization global stabilization set invariance parametric Lyapunov equation

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