H2/H∞ Control of Singularly Perturbed Systems: The State Feedback Case

The design of a mixed H2/H∞ linear state variable feedback (LSVF) suboptimal controller for a continuoustime singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index (PI) both are O(ε) close to those synthesized using the full order system. Each of the three algebraic matrix equations to be sequentially solved in our study, contains three matrix variables coupled in them. Two of these equations can be made independent of the matrix gain variable under mild restrictions.