On stability analysis of systems featuring a multiplicative combination of nonlinear and linear time-invariant feedback

Author

Kulkarni, Vishwesh V. ; Pao, Lucy Y. ; Safonov, Michael G.

Author_Institution

Dept. of Electr. Eng., Indian Inst. of Technol. Bombay, Mumbai, India

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

4036

Lastpage

4041

Abstract

We show that a set of sufficient conditions for the finite-gain stability of certain single-input-single-output (SISO) 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.

Keywords

feedback; linear systems; memoryless systems; nonlinear control systems; stability; Rantzer multiplier; SISO system; finite energy signal; finite-gain stability; linear time-invariant feedback; memoryless nonlinear feedback; positive memoryless monotone nonlinearities; single-input-single-output system; Convolution; Electronic mail; Equations; Linearity; Niobium; Stability analysis; Systems biology;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5717688

Filename

5717688