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7 Conclusions

  • He-Sheng Wang
  • Chee-Fai Yung
  • Fan-Ren Chang
Chapter
  • 431 Downloads
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 326)

Abstract

In this monograph, on the one hand, we have studied the \(\mathcal{H}_\infty\) 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.

Keywords

Descriptor System Algebraic Riccati Equation Dissipation Property Dissipation Inequality Balance Truncation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • He-Sheng Wang
    • 1
  • Chee-Fai Yung
    • 2
  • Fan-Ren Chang
    • 3
  1. 1.Department of Communications and Guidance Engineering National Taiwan Ocean University Keelung, Taiwan RoC, 20224 
  2. 2.Department of Electrical Engineering National Taiwan Ocean University Keelung, Taiwan RoC, 202 
  3. 3.Department of Electrical Engineering National Taiwan University Taipei, Taiwan RoC, 106 

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