Under the framework of the step-function method, the stability of a
nonlinear fuzzy hybrid control system combining an impulsive controller
and a continuous state feedback controller is investigated. Both the two
controllers are assumed to be subject to both actuator saturation and
time-varying delays, which has received little attention if any, in the
existing studies. A new assumption is established enabling the use of
generalized sector conditions to tackle the double saturation, and the
conservatism of the stability results is remarkably reduced thanks to
the improved step-function method. The stability theorem proposed in
this paper removes restriction on the time delays of both controllers,
which can be also applied to wider scopes of systems, including hybrid
control systems with both stabilizing and instabilizing impulses,
systems with varying impulsive gain, and systems with Zeno behavior.
Numerical simulations of stabilization for different systems by delayed
saturated hybrid control have been conducted, which demonstrate the
validity of proposed theorems.