Nonlinear time-varying feedback systems: ℒp-stability [1 ≤ p ≤ ∞]

An L
p
-stability criterion [
1 \leq p \leq \infty
] is given for a multi-input multi-output feedback system characterized by the functional equation
g = h + \bar{L}\bar{N}h
, when the linear operator
\bar{L}
is a convolution, whose kernel includes a sequence of delta functions, a polynomial term, and a finite number of increasing exponential terms, and when the nonlinear time-varying operator
\bar{N}
is memoryless. When
p = 2
, the primary ingredient of the criterion is a frequency-domain condition on the linear part of the system. This frequency-domain condition is the critical disk criterion when the system has only one input and one output.