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Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H infinity optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent observers avoid measurements of the plant outputs. We compare our coherent observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.

Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The proposed approach is fully constructive in the sense that suitable observer gains can be extracted from the solution of the optimization problems and is flexible enough to be extended to include performance constraints and parametric uncertainties. In order to be solvable, the infinite-dimensional linear programs are relaxed using a method based on sum of squares which is known to be asymptotically exact in the present case. Three examples are given for illustration: the first one pertains on the interval observation of an impulsive system under a minimum dwell-time constraint, the second one is about the interval observation of an aperiodic sampled-data system and the last one is about the interval observation of a linear switched system.

Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The proposed approach is fully constructive in the sense that suitable observer gains can be extracted from the solution of the optimization problems and is flexible enough to be extended to include performance constraints and parametric uncertainties. In order to be solvable, the infinite-dimensional linear programs are relaxed using a method based on sum of squares which is known to be asymptotically exact in the present case. Three examples are given for illustration: the first one pertains on the interval observation of an impulsive system under a minimum dwell-time constraint, the second one is about the interval observation of an aperiodic sampled-data system and the last one is about the interval observation of a linear switched system.