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Discretize this continuous time linear system
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[QUOTE="StoneTemplePython, post: 6005406, member: 613025"] to further simplify this, for now consider rescaling your matrix ##\mathbf A##. In particular divide everything by ##\lambda_1##. So ##\mathbf B := \frac{1}{\lambda_1}\mathbf A## You should notice that ##\mathbf B^3 = \mathbf B^5 = \mathbf B^7 = \mathbf B^9 ...## and ##-\mathbf B^3 = \mathbf B^4 = \mathbf B^6 = \mathbf B^8 = ... ## We could restate this in terms of Cayley Hamilton if you want, but try to work through the implications of the power series of ##e^{\mathbf B}## - - - - [U]Step two:[/U] [U][/U] After all that is done, consider the fact that for commuting matrices the exponential function behaves the same way as it does for 'regular numbers'. so ##e^{\lambda_1 \mathbf I}e^{\mathbf B} = e^{\lambda_1 \mathbf I \mathbf B} = e^{\lambda_1 \mathbf B} = e^{\mathbf A} ## where ##e^{\lambda_1 \mathbf I}## should be very easy to find [/QUOTE]
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Discretize this continuous time linear system
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