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parameter-dependent lyapunov functional for systems with multiple time delays

控制理论与应用（英文版） 2004年第3期2卷 239-245页

作者： MinWU YongHE SchoolofInformationScienceandEngineering CentralSouthUniversityChangshaHunan410083China SchoolofInformationScienceandEngineering CentralSouthUniversityChangshaHunan410083China／／SchoolofMathematicalScienceandComputingTechnologyCentralSouthUniversityChangshaHunan410083China

The separation of the lyapunov matrices and system matrices plays an important role when one uses parameter-dependent lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent lyapunov functional. The derivative term in the derivative of lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results.

关键词： Robust stability Delay-dependent parameter-dependent lyapunov functional Polytopic type uncertainties Linear matrix inequality

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Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent lyapunov functional approach

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控制理论与应用（英文版） 2006年第2期4卷 159-167页

作者： Ligang WU Changhong WANG Huijun GAO Qingshuang ZENG Space Control and Inertial Technology Research Center Harbin Instimt of Technology Harbin Heilongjiang 150001 China

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

关键词： parameter-dependent lyapunov functional Distributed delay systems Sliding mode control Robust stabilization Linear matrix inequalities (LMIs)

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