Parametric covariance assignment using a reduced-order closed-form covariance model

This paper presents a novel closed-form covariance model using covariance matrix decomposition for both continuous-time and discrete-time stochastic systems which are subjected to Gaussian noises. Different from the existing covariance models, it has been shown that the order of the presented model can be reduced to the order of original systems and the parameters of the model can be obtained by Kronecker product and Hadamard product which imply a uniform expression. Furthermore, the associated controller design can be simplified due to the use of the reduced-order structure of the model. Based on this model, the state and output covariance assignment algorithms have been developed with parametric state and output feedback, where the computational complexity is reduced and the extended free parameters of parametric feedback supply flexibility to the optimization. As an extension, the reduced-order closed-form covariance model for stochastic systems with parameter uncertainties is also presented in this paper. A simulated example is included to show the effectiveness of the proposed control algorithm, where encouraging results have been obtained.