The Robust H_∞ Control Of Singularly Perturbed Systems

In recent years, singular perturbation techniques have been widely applied in the area of control. On the other hand, the linear matrix (LMI) approach has been attracting more attention due to it extensively used in various control area. However, so far the control of singularly perturbed systems through LMI approach has not been used very widely. By considering this, in this paper the attention is focused on LMI-based approach to solving control problems for singularly perturbed systems. The approach eliminates the ill-conditioning caused by the interaction of slow and fast dynamic modes, the solutions to the problem are presented in terms of LMIs which are independent of the singular perturbationε.1) Using the LMI approach we obtain sufficient conditions of stability and stabilizability for singularly perturbed systems. An iterative algorithm is proposed for the design of stabilizing feedback controllers.2) The design of feedback controllers is investigated for nonlinear time-delay singularly perturbed systems described by T-S fuzzy model. Both state feedback and dynamic output feedback cases are considered. Sufficient conditions for nonlinear singularly perturbed systems to satisfy performance are derived. The approach avoids the ill-conditioned LMIs due to the interaction of slow and fast dynamic modes.3) Considering the problem of robust mean square stabilization and H∞control for a class of uncertain linear Markovian jump singularly perturbed systems with constant time delays in the states. Sufficient conditions of mean-square stabilized with a disturbance attenuation rateγfor the systems are given。Also, an algorithm is proposed for the design of stabilizing and H∞control feedback controllers.