Coherent robust \(H^\infty\) control of linear quantum systems with uncertainties in the Hamiltonian and coupling operators. (English) Zbl 1372.93096
Summary: This paper considers a class of uncertain linear quantum systems subject to uncertain perturbations both in the system Hamiltonian and in the coupling operators. A sufficient condition is provided such that these uncertain quantum systems can be guaranteed to be robustly strict bounded real with a given disturbance attenuation parameter. A scaled \(H^\infty\) problem is shown to have a connection with the stability of the given uncertain quantum system and can be used as an auxiliary system to design a robust \(H^\infty\) quantum controller. A pair of Riccati equations is used to give explicit formulas for the parameters of a desired controller. Illustrative examples show that for the given uncertain quantum system, the method presented in this paper has improved performance over the existing quantum \(H^\infty\) control results without considering uncertainties.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93B35 | Sensitivity (robustness) |
| 81Q93 | Quantum control |
| 93C05 | Linear systems in control theory |
| 93C41 | Control/observation systems with incomplete information |
Keywords:
coherent robust \(H^\infty\) control; quantum control; linear quantum systems; uncertaintiesReferences:
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