Multiplier analysis of Lurye systems with power signals
CoRR(2024)
摘要
Multipliers can be used to guarantee both the Lyapunov stability and
input-output stability of Lurye systems with time-invariant memoryless
slope-restricted nonlinearities. If a dynamic multiplier is used there is no
guarantee the closed- loop system has finite incremental gain. It has been
suggested in the literature that without this guarantee such a system may be
critically sensitive to time-varying exogenous signals including noise. We show
that multipliers guarantee the power gain of the system to be bounded and
quantifiable. Furthermore power may be measured about an appropriate steady
state bias term, provided the multiplier does not require the nonlinearity to
be odd. Hence dynamic multipliers can be used to guarantee Lurye systems have
low sensitivity to noise, provided other exogenous systems have constant steady
state. We illustrate the analysis with an example where the exogenous signal is
a power signal with non-zero mean.
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