A revisited Tsypkin criterion for discrete-time nonlinear Lur'e systems with monotonic sector-restrictions
SCIE
SCOPUS
- Title
- A revisited Tsypkin criterion for discrete-time nonlinear Lur'e systems with monotonic sector-restrictions
- Authors
- Park, P; Kim, SW
- Date Issued
- 1998-11
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- Abstract
- This paper revisits a well-known Tsypkin criterion for stability analysis of discrete-time nonlinear Lur'e systems. When nonlinearities are monotonic and sector restricted by [0, <(Delta)over bar>], where <(Delta)over bar> is positive definite, it is shown by Kapila and Haddad that the system is absolutely stable if a function G(0)(z) = <(Delta)over bar>(-1) + {I + (1 - z(-1))K+}G(z) is strictly positive real, where K+ is nonnegative diagonal and G(z) represents a transfer function of the linear part of the Lur'e system with invertible or identically zero G(0). This paper extends this criterion when <(Delta)over bar> is positive diagonal, by choosing a new Lyapunov function to obtain an LMI criterion. From a frequency-domain interpretation of this LMI criterion, another sufficient criterion is generated which establishes that the system is absolutely stable if a function G(0)(z) = <(Delta)over bar>(-1) + {I + (1 - z(-1)) K+ + (1 - z)K-} G(z) is strictly positive real, where K+ and K- are nonnegative diagonal and orthogonal to each other. (C) 1998 Elsevier Science Ltd. All rights reserved.
- Keywords
- robust stability; nonlinear system; LYAPUNOV
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/20578
- DOI
- 10.1016/S0005-1098(98)00100-9
- ISSN
- 0005-1098
- Article Type
- Article
- Citation
- AUTOMATICA, vol. 34, no. 11, page. 1417 - 1420, 1998-11
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