\(H^{2}\) optimal control for linear stochastic systems
The aim of the paper is to provide an optimal solution to the \(H^2\) state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case, the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case, the optimal \(H^2\) controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical examples allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature.
scientific article; zbMATH DE number 2105467
scientific article