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On Lyapunov-Krasovskii Functionals for Switched Nonlinear Systems with Delay
We present a set of results concerning the existence of Lyapunov-Krasovskii
functionals for classes of nonlinear switched systems with time-delay. In
particular, we first present a result for positive systems that relaxes
conditions recently described in \cite{SunWang} for the existence of L-K
functionals. We also provide related conditions for positive coupled
differential-difference positive systems and for systems of neutral type that
are not necessarily positive. Finally, corresponding results for discrete-time
systems are described.Comment: 19 Page
Functions of perturbed operators
We prove that if 0<\a<1 and is in the H\"older class \L_\a(\R), then
for arbitrary self-adjoint operators and with bounded , the
operator is bounded and \|f(A)-f(B)\|\le\const\|A-B\|^\a. We
prove a similar result for functions of the Zygmund class \L_1(\R):
\|f(A+K)-2f(A)+f(A-K)\|\le\const\|K\|, where and are self-adjoint
operators. Similar results also hold for all H\"older-Zygmund classes
\L_\a(\R), \a>0. We also study properties of the operators for
f\in\L_\a(\R) and self-adjoint operators and such that belongs
to the Schatten--von Neumann class \bS_p. We consider the same problem for
higher order differences. Similar results also hold for unitary operators and
for contractions.Comment: 6 page
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