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ps 7 604 - Problem 5 Consider the linear system d dt x t =...

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ECE 604 LINEAR SYSTEMS Problem Set #7 Issued: Thursday, November 19, 2009 Due: Thursday, December 3, 2009 Problem 1: Compute the minimal realization for the sequence of Markov parameters g 0 = 0 g 1 = 1 g 2 = ! 4 g 3 = 16 g 4 = ! 64 g 5 = 256 ... Problem 2: Rugh, Problem 6.3, p. 125. Problem 3: Rugh, Problem 6.7, p. 111. Problem 4: Rugh, Problem 6.11, p. 112.
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Unformatted text preview: Problem 5: Consider the linear system d dt x t ( ) = 1 1 + t x t ( ) x ( ) = x with the function V x , t ( ) = e ! 3 t x 2 a) Show that d dt V x , t ( ) solutions ! " t # b) Is V x , t ( ) a Lyapunov function? Can we conclude that the system is stable? c) Is the system stable?...
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