Global stabilization of nonlinear systems by quadratic Lyapunov functions |
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Authors: | I E Zuber A Kh Gelig |
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Institution: | (1) Department of Production Engineering, Thermoenergetics, and Mathematical Models, University of Genova, Genova, Italy;(2) Institute of Intelligent Systems for Automation, National Research Council of Italy, Genova, Italy;(3) Department of Communications, Computer, and System Sciences, University of Genova, Genova, Italy |
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Abstract: | The system x = A (t, x)x + B(t, x)u, where A(t, x) and B(t, x) are, respectively, n × n and n × m (m<n) continuous matrices whose elements are uniformly bounded for t ≽ t
0 and x ∈ ℝ
n
, is considered. It is assumed that the system has relative degree q = n - m + 1, and the determinant of the matrix composed of the last m rows of the matrix B(t, x) is bounded away from zero for t ≽ t
0 and x ∈ ℝ
n
. A special quadratic Lyapunov function with constant positive definite coefficient matrix H depending only on the range of variation of the coefficients in the matrices A(t, x) and B(t, x) is constructed and applied to obtain a control u(t, x) =7n ~B⋆ (t, x)H depending on a scalar parameter 7n under which the system is globally asymptotically stable provided that it is closed. Here,
~B (t, x) is the scalar matrix obtained from the matrix B(t, x) by setting the first n - m rows to zero. |
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Keywords: | |
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