{
  "seed": 7,
  "system": {
    "A": 0.2,
    "B": 1.0,
    "C": 1.0,
    "D": 0.0,
    "rho": 0.99,
    "horizon": 400
  },
  "math_check": {
    "closed_loop_ratio_predicted": 0.5,
    "closed_loop_ratio_observed": 0.5,
    "max_ratio_error": 0.0
  },
  "comparison": {
    "baseline_L0_gain": 1.0206207261596576,
    "idea_L06_gain": 1.6666666666666667,
    "idea_certificate_gamma": 5.128535538220312,
    "idea_over_baseline_gain_ratio": 1.632993161855452
  },
  "predictions": {
    "boundary_predicted_L": 0.8,
    "boundary_observed_first_unstable_L": 0.81,
    "boundary_grid_rows": [
      {
        "L": 0.0,
        "empirical_l2_gain": 1.0206207261596576,
        "analytic_l2_gain": 1.0206207261596576,
        "certificate_gamma": 1.2582154827832464,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.2,
        "empirical_l2_gain": 1.0910894511799618,
        "analytic_l2_gain": 1.0910894511799618,
        "certificate_gamma": 1.680707756725894,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.4,
        "empirical_l2_gain": 1.25,
        "analytic_l2_gain": 1.25,
        "certificate_gamma": 2.5317260923139813,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.6,
        "empirical_l2_gain": 1.6666666666666667,
        "analytic_l2_gain": 1.666666666666667,
        "certificate_gamma": 5.128535538220312,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.75,
        "empirical_l2_gain": 3.2025630761017427,
        "analytic_l2_gain": 3.202563076101742,
        "certificate_gamma": 22.469625350236743,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.79,
        "empirical_l2_gain": 7.087646678417917,
        "analytic_l2_gain": 7.088812050083354,
        "certificate_gamma": 200.5037818054957,
        "certificate_feasible": true,
        "status": "scipy-slsqp",
        "stable_analytic": true
      },
      {
        "L": 0.81,
        "empirical_l2_gain": 373.725537945458,
        "analytic_l2_gain": Infinity,
        "certificate_gamma": NaN,
        "certificate_feasible": false,
        "status": "scipy-slsqp infeasible",
        "stable_analytic": false
      },
      {
        "L": 0.9,
        "empirical_l2_gain": 7.1543755041161096e+16,
        "analytic_l2_gain": Infinity,
        "certificate_gamma": NaN,
        "certificate_feasible": false,
        "status": "scipy-slsqp infeasible",
        "stable_analytic": false
      },
      {
        "L": 1.0,
        "empirical_l2_gain": 5.910045640679525e+31,
        "analytic_l2_gain": Infinity,
        "certificate_gamma": NaN,
        "certificate_feasible": false,
        "status": "scipy-slsqp infeasible",
        "stable_analytic": false
      },
      {
        "L": 1.2,
        "empirical_l2_gain": 2.0603956252812265e+58,
        "analytic_l2_gain": Infinity,
        "certificate_gamma": NaN,
        "certificate_feasible": false,
        "status": "scipy-slsqp infeasible",
        "stable_analytic": false
      }
    ],
    "epsilon_linear_fit_slope": 1.2500000000000007,
    "epsilon_zero_norm": 0.0,
    "epsilon_norms": {
      "0.0": 0.0,
      "0.25": 0.3125,
      "0.5": 0.625,
      "1.0": 1.25,
      "2.0": 2.5
    },
    "epsilon_prediction": "state l2 norm is proportional to one-sample disturbance epsilon",
    "certificate_prediction": "feasible IQC gamma upper-bounds empirical l2 gain"
  }
}