Analysis And Synthesis On Stability, Stabilizability And Detectability For 2-D Singular Systems

This dissertation concerns the stability, stabilizability and detectability of 2-D singular systems.In part one, the focus is on the internal stability of 2-D singular systems. First, based on the existing results of Inner stability of 2-D SGM, one hypothesis about the internal stability of 2-D acceptable system is proved and the concept internal stability is extended to the 2-D singular case. Then the Lyapunov approach for stability analysis is generalized to the singular case and the Lyapunov equations of 1-D and 2-D singular systems are established. At last the concept internal stability is extended to the system with delays described by 2-D singular Roesser model and the necessary and sufficient conditions of internal stability of such system are obtained.In part two, the focus is on the stabilizability and detectablity of 2-D singular systems. Necessary and sufficient conditions for stabilizability and detectablity of 2-D singular systems are obtained respectively, and the relationship between BIBO stability and internal stability is discussed based on this conditions. The observer design procedures are also provided. One is on designing general asymptotic observer for detectable 2-D singular system, and another is on designing a class of full order asymptotic observer for 2-D singular systems. Meanwhile, the properties of the state feedback systems that contain observers are obtained.In part three, the optimal control of 2-D discrete linear systems described by FMM II is solved using dynamic programming, and the exact model matching for 2-D singular Roesser model is discussed.All the procedures are illustrated by the examples.