Predictor-Based Control of Systems With State Multiplicative Noise

The problem of H∞ state-feedback control of linear continuous-time systems with state multiplicative noise in the presence of input delay is investigated. A predictor-based control is applied, for the first time, to these systems. A new condition for stability is derived in a form of a linear matrix inequality. The latter condition is extended to one that guarantees a prescribed L
₂
-gain bound for the stochastic system. Solutions are obtained for both constant and time-varying delays. Because of the multiplicative noise, the predictor-based control cannot stabilize the system for arbitrarily large delay. It admits, however, delays that are significantly larger than the delays that can be treated by the corresponding non-predictive state-feedback control. The theoretical results are demonstrated by two examples. The first example shows the advantage of the predictor-based controller and the second one demonstrates the applicability of the theory to process control systems.