Stability Analysis Of Reset Observer Under Singular System

Reset systems, as a special type of hybrid systems, have a wide range of practical background and important significance. Due to the interaction between the continu-ous dynamic and the discrete dynamic, the dynamical behaviors of reset systems are very complicated. Many problems of analysis and syntheses need to be studied. By introducing reset element into the design of the state observer, this thesis studies the design problems of the state observer for singular single-input single-output (SISO) systems and singular multi-input multi-output (MIMO) systems, respectively. First, for these two types of systems, the reset observer models are provided, then, the stability and the convergence are analyzed. The main contributions are as follows.(1) By introducing the reset element into the singular SISO system and the singular MIMO systems, the reset observers are established. Then, the singular predict error system and the singular predict dynamic expanding equation are given based on different properties of different systems.(2) By constructing a appropriate Lyapunov function and using linear ma-trix inequality (LMI) method and S-Pocedure theory, the sufficient conditions of quadratic stability and input-output stability for these two types of systems are provided, respectively. Numerical examples show the effectiveness of the conclusion.(3) The L2-gain of the reset observer for both the singular SISO system and the singular MIMO systems are defined, and a method of adjusting the L2gain is presented. The method can effectively prevent the overshoot amount and can be calculated simply, and therefore the operability of the method is high.