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Unformatted text preview: Show that the origin of (1) is asymptotically stable if in a neighborhood of the origin, there is a continuous positive denite function V ( x ) so that V ( x ) is negative denite. Consider the linear discretetime system: x k +1 = Ax k . Show that the following statements are equivalent: * x = 0 is asymptotically stable. *  i  &lt; 1 for all eigenvalues of A . * Given any Q = Q T &gt; 0, there exists P = P T &gt; 0, which is a unique solution to the linear equation A T PAP =Q ....
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 Fall '09
 Marsden
 Lyapunov stability, Structural stability, Discretetime dynamical systems, Equations and Dynamical Systems

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