On stability analysis of systems featuring a multiplicative combination of nonlinear and linear time‐invariant feedback |
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| Authors: | Vishwesh V. Kulkarni Lucy Y. Pao Michael G. Safonov |
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| Affiliation: | 1. Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 400 076, India;2. Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80302, U.S.A.;3. Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089‐2563, U.S.A. |
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| Abstract: | We show that sufficient conditions for the finite‐gain stability of certain systems featuring a multiplicative combination of memoryless nonlinear feedback and linear time‐invariant feedback, as encountered in some systems' biology prototype applications, can be obtained by building on the Rantzer multipliers. These results are obtained by observing that for all finite energy signals x, the time‐truncated inner product 〈x, H(x)N(x)〉T is positive for all T>0 if N belongs to a subclass of positive memoryless monotone nonlinearities and if, in addition, H is a Rantzer multiplier. Copyright © 2011 John Wiley & Sons, Ltd. |
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| Keywords: | stability multipliers monotone nonlinearities Zames– Falb multipliers |
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