Non-fragile Consistency Control of Covariance/H∞ Indices for a Class of Linear Periodic Systems

For the case of perturbed controller parameter, the non-fragile consistency problem of steady state covariance and robust H_infin indices for a class of linear continuous periodic systems is investigated. The periodic system described by the interval form is transformed to the linear uncertain system first, based on the tool of linear matrix inequality (LMI), then the following problems are settled: the minimum lower bound for the steady state covariance when the system is asymptotically stable; the minimum lower bound for the robust H_infin consistent with the given steady state variance; the design algorithm for the non-fragile satisfactory controller is given under the consistent steady state covariance and H_infin indices constraints. Finally the conclusion is illustrated by the numerical example