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Title: Frequency-domain L 2-stability conditions for switched linear and nonlinear SISO systems
Authors: Huang, Z.H.
Venkatesh, Y.V. 
Xiang, C. 
Lee, T.H. 
Keywords: absolute stability
circle criterion
feedback systems
KPY lemma
Lur'e problem
multiplier functions
Nyquist's criterion
periodic coefficient systems
switched systems
time-varying systems
Issue Date: 1-Mar-2014
Citation: Huang, Z.H., Venkatesh, Y.V., Xiang, C., Lee, T.H. (2014-03-01). Frequency-domain L 2-stability conditions for switched linear and nonlinear SISO systems. International Journal of Systems Science 45 (3) : 682-701. ScholarBank@NUS Repository.
Abstract: We consider the L 2-stability analysis of single-input-single- output (SISO) systems with periodic and nonperiodic switching gains and described by integral equations that can be specialised to the form of standard differential equations. For the latter, stability literature is mostly based on the application of quadratic forms as Lyapunov-function candidates which lead, in general, to conservative results. Exceptions are some recent results, especially for second-order linear differential equations, obtained by trajectory control or optimisation to arrive at the worst-case switching sequence of the gain. In contrast, we employ a non-Lyapunov framework to derive L 2-stability conditions for a class of (linear and) nonlinear SISO systems in integral form, with monotone, odd-monotone and relaxed monotone nonlinearities, and, in each case, with periodic or nonperiodic switching gains. The derived frequency-domain results are reminiscent of (i) the Nyquist criterion for linear time-invariant feedback systems and (ii) the Popov-criterion for time-invariant nonlinear feedback systems with the Lur'e-type nonlinearity. Although overlapping with some recent results of the literature for periodic gains, they have been derived independently in essentially the Popov framework, are different for certain classes of nonlinearities and address some of the questions left open, with respect to, for instance, the synthesis of the multipliers and numerical interpretation of the results. Apart from the novelty of the results as applied to the dwell-time problem, they reveal an interesting phenomenon of the switched systems: fast switching can lead to stability, thereby providing an alternative framework for vibrational stability analysis. © 2014 Taylor and Francis.
Source Title: International Journal of Systems Science
ISSN: 00207721
DOI: 10.1080/00207721.2012.724199
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