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In this paper the absolute stability of 2nd order discrete-time single variable Lur'e systems is investigated. Simple sufficient conditions for the existence of a common unic Lyapunov function are presented. A necessary condition for the existence of a common unic Liapunov function for 2nd order discrete Lur'e systems is expressed as a simple restriction on the root locus of the system.
In this paper sufficient conditions for the absolute stability of 2nd order single variable Lur'e systems with finite sector nonlinearities are presented. These conditions are expressed as simple restrictions on the root locus of the system. For higher order systems, numerical evidence is presented to establish absolute stability.
Necessary and sufficient conditions for the existence of a common piecewise quadratic Liapunov function for n-D single variable Lur'e systems are stated in terms of LMI's and a sufficient condition is stated in terms of a frequency domain inequality. Hence a simple analytic necessary condition for absolute stability of n-D systems is established. Numerical evidence is presented to establish the absolute...
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