State Feedback Based on Consistency Analysis of Pole and Output-Variance Constraints

This paper studies satisfactory state feedback control for a class of linear stochastic systems so that resulting closed loop systems satisfy pre specified circular pole and output variance constraints simultaneously. The consistency of constraint indices for output variance and pole is analyzed first. By means of linear matrix inequality (LMI) approach, a good range is presented for output variance upper bound (and lower bound) index that is consistent to a given pole index. Then a control design theory is proposed for considered systems with consistent circular pole index and upper bound index of output variance, furthermore, a control design technique is provided as the output variance index is specified in terms of a certain region. Finally an example is given to illustrate the results obtained and the design scheme provided.