All stabilizing and concealing Gaussian type controllers for linear scalar systems

In order to conceal the information of the state of a given system, this paper adds an artificial noise called a privacy input to the state. The privacy input is designed as a Gaussian random variable with the mean zero and the time varying variance, i.e., the variance is a design variable. In order to measure confidentiality of the state, the paper uses the mutual information of the state and the output which is the perturbed state by the privacy input. The article formulates a problem which finds all controllers such that a given linear scalar system is mean square asymptotically stable and satisfies a given confidential level of the state. Simulation results demonstrate that solutions of the problem are useful to conceal the information of the transient state.