Reliability-based robust H∞ control of linear systems with uncertain parameters

Uncertainty of the parameters in control system was described by interval variables, and some idea of the nonprobabilistic reliability method that we proposed in previous papers was used for the robust performance analysis and synthesis of uncertain systems. A new method, called robust reliability method, was presented for robust H_∞ control performance analysis and robust feedback controller design of the linear systems with uncertain parameters. By the method, robust reliability measure of an uncertain control system satisfying a specified control performance can be obtained, and the robustness bounds of the uncertain parameters can be provided. The optimal control strategies were derived by minimizing the disturbance attenuation index and the required energy for control, coordinately, with the constraints on robust reliability of the system. The presented formulations for analysis and synthesis of control systems are within the framework of linear matrix inequality (LMI), which makes it quite convenient to implement. A numerical example was provided to demonstrate the validity and feasibility of the presented method.