Computational geometry : algorithms and applications by Mark de Berg; et al

By Mark de Berg; et al

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Korayem and R. ⎤ ⎥ ⎥ , (15) J 4 ⎥⎦ J 2 − 2 J 3 +J 4 J 3 − J 4 +X 2 Cq3 where J ( q ) is a symmetric matrix. Substituting Equation (14) into Equation (13) yields L(q, q ) = cJ −1 ⎡ 1 −1 0 ⎤ ⎢0 1 −1⎥ . ⎢ ⎥ ⎣⎢0 0 1 ⎥⎦ (16) Since J ( q ) is positive definite for all q , a Lyapunov candidate for the observer given in Equations (10) and (11) can be chosen as follow V (e, q ) = e J (q )e . T (17) The time derivative of the Lyapunov function along the observer trajectory is dV (e, q ) dt = ∂V (e, q ) ∂e e+ ∂V (e, q ) ∂q q.

He has published nearly 87 papers in china and international journals and 3 books. He has won the First Class Award from Ministry of Mechanical Industry, the First Class Award from Ministry of Electrical Industry, the Second Class Award from Ministry of Aeronautics and the Second Award from Beijing Government, and the National Science Fund for Distinguished Young Scholar. He has also been awarded the “Mao Yisheng” Beijing young science and technology nominated award and the “Rong Hong” education of science and technology award by the American United Technologies.

In the conventional disturbance observer design, the algorithm consists of an inverse of nominal model of the plant dynamics, and a low pass-filter. If the plant has nonminimum phase zeros, then the disturbance observer must be internally unstable. Even for strictly proper systems, the disturbance observer includes derivative operation. So, the high-frequency noise might be amplified. However, using Internal Model (IM), these kinds of problems would be removed [8]. Another technique in disturbance estimation problem which can be applied to both linear and nonlinear systems is state observer design for augmented system.

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