Constructive stabilization for quadratic input nonlinear systems

Authors:
Jianghua Zhong;Daizhan Cheng;Xiaoming Hu
Affiliations:
Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, PR China and Optimization and Systems Theory, Royal Institute of Technology, 100 44 Stockholm, Sweden;Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, PR China;Optimization and Systems Theory, Royal Institute of Technology, 100 44 Stockholm, Sweden
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.