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Mathematical Models Admitting Diagonal-Type Liapunov Functions

In: Matrix Diagonal Stability in Systems and Computation

Author

Listed:
  • Eugenius Kaszkurewicz

    (Federal University of Rio de Janeiro, COPPE/UFRJ, Department of Electrical Engineering)

  • Amit Bhaya

    (Federal University of Rio de Janeiro, COPPE/UFRJ, Department of Electrical Engineering)

Abstract

The objective of this chapter is to introduce classes of dynamical systems that admit diagonal-type Liapunov functions and give the basic stability results, which are used in the remaining application-oriented chapters of the book. The word diagonal recalls that the prototypical function of this class is the quadratic form x T Px, where P is a positive diagonal matrix and x a real vector. The results are stated in the most general form, without the additional hypotheses or assumptions that arise from the specifics of applications. Material on continuous-and discrete-time systems is classified in different, independent sections.

Suggested Citation

  • Eugenius Kaszkurewicz & Amit Bhaya, 2000. "Mathematical Models Admitting Diagonal-Type Liapunov Functions," Springer Books, in: Matrix Diagonal Stability in Systems and Computation, chapter 3, pages 90-127, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1346-8_3
    DOI: 10.1007/978-1-4612-1346-8_3
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