Andrey V. Sarychev
Departamento de Matematica,
Universidade de Aveiro, Aveiro, 3810-193, Portugal
Lie-algebraic methods for stability analysis of time-variant systems
We suggest an approach to asymptotic analysis of the flows generated by time-periodic
(linear and nonlinear)
systems.
We utilize the approach -
a kind of high-order averaging or homogenization - for studying stability
and asymptotic stability
of these systems
and also for the design of time-variant
stabilizers.
The computation of the high-order averagings
is based on the tools of Lie and
chronological algebras.
Various examples are arranged in order to
illustrate the approach. Those include
second- and third-order linear ODE with periodic coefficients,
nonlinear ODE under homogeneity assumptions,
time-variant stabilizers for
bilinear and nonlinear nonholonomic systems.
Abstract in Postscript
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