7 Conclusions

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• 作者：He-Sheng Wang ; Chee-Fai Yung ; Fan-Ren Chang
• 刊名：Lecture Notes in Control and Information Sciences
• 出版年：2006
• 出版时间：2006
• 年：2006
• 卷：326
• 期：1
• 页码：pp.137-140
• 全文大小：172 KB

文摘

In this monograph, on the one hand, we have studied the H_£¤\mathcal{H}_\infty control problems for dynamical systems governed by a set of differential-algebraic equations, in an inclusive manner. It has been shown that most of the existing results for conventional state-variable systems can be extended, under appropriate assumptions, to descriptor systems. On the other hand, we have examined certain properties of the DAEs, which include the solvability, stability, controllability, observability, and dissipativeness. Some useful preliminary results have been first developed in Chapter 2. We have derived the Lyapunov stability theorem and LaSalle’s Invariant Principle for stability test of descriptor systems. Furthermore, the dissipation property has been investigated in the descriptor systems context. It has been shown that the dissipation property can be characterized by the dissipation inequality, which turn out a Hamilton– Jacobi inequality for the nonlinear case or a generalized algebraic Riccati inequality for the linear case.