how does the command "nd2sys"work ?

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dipan 2012-2-23

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https://ww2.mathworks.cn/matlabcentral/answers/30009-how-does-the-command-nd2sys-work

编辑： Ray Huang 2017-5-8

Hi, I am trying to make the generalized plant for a Hinfinity control problem. In one of the examples I see that "nd2sys" is used to convert a transfer function ([num],[den]) into a [A B; C D] like state space form called the System Matrix. Could anyone provide an explanation of how this function works because it also adds an extra row and column in the matrix which I cant figure out why ?

thanks, dipan

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Answer 1

Ray Huang 2017-5-8

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https://ww2.mathworks.cn/matlabcentral/answers/30009-how-does-the-command-nd2sys-work#answer_266046

编辑：Ray Huang 2017-5-8

The extra row and column are added for the data structure information. The -inf in the bottom right means the matrix is a SYSTEM matrix. The number in the top right denotes the number of system state. That is, no matter which function you use, if the function output is SYSTEM matrix, there will always have extra row and column.

For example, if we have a system y=(1/s)*u, then we can get the state-space model x'=Ax+Bu y=Cx+Du where A=0,B=1,C=1,D=0. It is easy to see that the model only have one system state, and the result of "nd2sys" should be [A B 1;C D 0;0 0 -Inf]