Application of sub-predictor control for linear delayed stochastic systems

The problem of robust predictor-based H_∞ state-feedback control for uncertain continuous-time stochastic state-multiplicative retarded systems is extended to include a set of sub-predictors, thus considerably improving the control performance. The multiplicative noise appears in the system dynamic matrix and in the measurement matrix of the observed signal, while the delay resided in the input to the system. In this problem, a cost function is defined which is the expected value of the standard H_∞ performance index with respect to the uncertain parameters. In the robust case, the solution is obtained via a simple set of linear matrix inequalities. We bring a detailed numerical example that demonstrates the superiority of designing state-feedback control via a set of sub predictor compared to a single predictor design.