Aiming at enhancing the quality as well as the reliability of synchronization, this paper is concerned with the fault detection issue within the synchronization process for a class of nonlinear systems in the existence of external disturbances. To handle such problems, the concept of robust fault-sensitive （RFS） synchronization is proposed, and a method of determining such a kind of syncbronization is developed. Under the framework of RFS synchronization, the master and the slave systems are robustly synchronized, and at the same time, sensitive to possible faults based on a mixed H_/H~ performance. The design of desired output feedback controller is realized by solving a linear matrix inequality, and the fault sensitivity H index can be optimized via a convex optimization algorithm. A master-slave configuration composed of identical Chua＇s circuits is adopted as a numerical example to demonstrate the effectiveness and applicability of the analytical results.
For a stabilizable system, the extension of the control inputs has no use for stabilizability, but it is important for optimal control. In this paper, a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions. A similar result is also provided for H2 optimal control problem. These results show an essential difference between single-input and multi-input control systems. Several examples are taken to illustrate related problems.
