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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"bug: delayed dirac input not considered in forced_response","articleBody":"Hi,\n\nI have encountered a strange issue using the function forced_response with a NonlinearIOSystem object:\n\nWhen applying a dirac as input, if the dirac is applied after too much time after the beginning of the simulation, the response of the system does not include its impact.  \nHere is a small piece of code to reproduce the issue:\n\n```\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport control\n\ndef dynamic_function(t, x, u, param=None):\n    \"\"\"\n    Dynamic function for the system.\n    \"\"\"\n    A = np.array([[0, 1], [-1, -1]])\n    B = np.array([[0], [1]])\n    return A @ x + B @ u\n\ndef output_function(t, x, u, param=None):\n    \"\"\"\n    Output function for the system.\n    \"\"\"\n    C = np.array([[1, 0]])\n    return C @ x\n\nsys = control.NonlinearIOSystem(\n    dynamic_function, output_function,\n    inputs=1,\n    outputs=1,\n    states=2\n    )\n\nt = np.linspace(0, 10, 100)\nu = np.zeros_like(t)\n\n\ndirac_index = 6\n\n\nu[dirac_index] = 1  # Dirac input at t=0\n\nresults = control.forced_response(sys, T=t, U=u)\n\nplt.figure()\nplt.plot(t, results.y[0], label='Output')\nplt.title('Response of Nonlinear System to Dirac Input')\nplt.xlabel('Time (s)')\nplt.ylabel('Output')\nplt.grid()\nplt.legend()\nplt.show()\n```\n\nIf dirac_index is inferior or equal to 5, the normal output is obtained while if dirac_index is superior to 6, both the output and the state of the function are null for the whole simulation time.\n\nHere are the installed package:\n├── control v0.10.1\n│   ├── matplotlib v3.10.3 \n│   ├── numpy v2.2.5\n│   └── scipy v1.15.3\n\nUsing python 3.12.3.","author":{"url":"https://github.com/BobAubouin","@type":"Person","name":"BobAubouin"},"datePublished":"2025-06-05T10:32:25.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":2},"url":"https://github.com/1152/python-control/issues/1152"}