Decentralized coherent robust H^∞ control of a class of large-scale uncertain linear complex quantum stochastic systems

Strict Bounded Real Decentralized Coherent Quantum Robust H∞ Control

“…, k); z is an n z ×1 vector of controlled outputs; and y is an n y ×1 vector of 'measurement' outputs. All the coefficient matrices in (1) are complex matrices with compatible dimensions corresponding to the dimensions of the operators and signals in (1); see James et al (2008); Nurdin et al (2009); Maalouf and Petersen (2009).…”

“…Applying a non-decentralized coherent quantum controller to a large-scale quantum system may require expensive computation and implementation. This concern has motivated Harno and Petersen (2010) to propose a method to construct a decentralized coherent quantum robust H ∞ controller for a class of large-scale linear complex quantum stochastic systems with structured uncertainties. Here, the dynamics of a quantum system is determined only by annihilation operators and represented in terms of linear quantum stochastic differential equations (QSDEs); e.g., see Maalouf and Petersen (2009).…”

“…Here, the dynamics of a quantum system is determined only by annihilation operators and represented in terms of linear quantum stochastic differential equations (QSDEs); e.g., see Maalouf and Petersen (2009). However, the method in Harno and Petersen (2010) does not always lead to a stable and strict bounded real decentralized quantum robust H ∞ controller, which may not be physically realizable.…”

“…In this paper, we propose a new method to synthesize a stable and strict bounded real decentralized coherent quantum robust H ∞ controller, which is always physically realizable, for the same class of quantum systems as in Harno and Petersen (2010). There are two main ideas underlying our approach.…”

“…First, we do not treat interconnections between quantum subsystems as uncertainties, but rather the neglected off-diagonal parts of the transfer function matrix of the non-decentralized quantum controller are treated as uncertainties. This allows the decentralized coherent quantum controller to exploit the interconnections, which are assumed to be known; e.g., see Harno and Petersen (2010). Second, we introduce an additional ⋆ Research supported by the Australian Research Council (ARC) and Air Force Office of Scientific Research (AFOSR).…”