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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"modal canonical form does not work with repeated eigenvalues","articleBody":"The `modal_form()` function appears to assume that all eigenvalues are distinct.  The following example gives strange results:\r\n```\r\nimport control as ct\r\nsys_repeat = ct.StateSpace([[-1, 1], [0, -1]], [[0], [1]], [[1, 0]], [[0]])\r\nsys_modal, T = ct.modal_form(sys_repeat)\r\nprint(sys_modal)\r\n```\r\nwhich yields\r\n```\r\nA = [[-1.00000000e+00  0.00000000e+00]\r\n [ 2.22044605e-16 -1.00000000e+00]]\r\n\r\nB = [[4.50359963e+15]\r\n [4.50359963e+15]]\r\n\r\nC = [[-1.  1.]]\r\n\r\nD = [[0.]]\r\n```\r\nThe problem is that the transformation `T` as computed in `modal_form` is singular:\r\n```\r\n[[-1.00000000e+00  1.00000000e+00]\r\n [ 2.22044605e-16  0.00000000e+00]]\r\n```\r\n","author":{"url":"https://github.com/murrayrm","@type":"Person","name":"murrayrm"},"datePublished":"2019-06-23T23:23:45.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":3},"url":"https://github.com/318/python-control/issues/318"}