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"""Hinf design using hinfsyn.

Demonstrate Hinf design for a SISO plant using h2syn. Based on [1], Ex. 7.

[1] Scherer, Gahinet, & Chilali, "Multiobjective Output-Feedback Control via

LMI Optimization", IEEE Trans. Automatic Control, Vol. 42, No. 7, July 1997.

"""

# %%

# Packages

import numpy as np

import control

# %%

# State-space system.

# Process model.

A = np.array([[0, 10, 2],

[-1, 1, 0],

[0, 2, -5]])

B1 = np.array([[1],

[0],

[1]])

B2 = np.array([[0],

[1],

[0]])

# Plant output.

C2 = np.array([[0, 1, 0]])

D21 = np.array([[2]])

D22 = np.array([[0]])

# Hinf performance.

C1 = np.array([[1, 0, 0],

[0, 0, 0]])

D11 = np.array([[0],

[0]])

D12 = np.array([[0],

[1]])

# Dimensions.

n_x, n_u, n_y = 3, 1, 1

# %%

# Hinf design using hinfsyn.

# Create augmented plant.

Baug = np.block([B1, B2])

Caug = np.block([[C1], [C2]])

Daug = np.block([[D11, D12], [D21, D22]])

Paug = control.ss(A, Baug, Caug, Daug)

# Input to hinfsyn is Paug, number of inputs to controller,

# and number of outputs from the controller.

K, Tzw, gamma, rcond = control.hinfsyn(Paug, n_y, n_u)

print(f'The closed-loop H_inf norm of Tzw(s) is {gamma}.')

# %%

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