Mathematical Models Admitting Diagonal-Type Liapunov Functions

Eugenius Kaszkurewicz and Amit Bhaya
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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

Chapter 3 in Matrix Diagonal Stability in Systems and Computation, 2000, pp 90-127 from Springer

Abstract: 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.

Keywords: Exponential Stability; Interval Matrix; Liapunov Function; Interval Matrice; Positive Diagonal Matrix (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-1346-8_3

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