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STABILITY AND CONTROL OF TIME—DELAY
SWITCH NONLINEAR SYSTEMS
ABSTRACT
In the past decades, the research related to nonlinear systems has
received considerable attention. Stability and H ∞ control problem of
nonlinear systems play an important role in the field of control
engineering. In this paper, we focus on switch nonlinear system.
Lyapunov-Krasovskii functional, stochastic analysis and linear matrix
inequality approaches are combined to investigate the problem of robust
stability of delay Hopfield neural network and H ∞ control of a class of
delay Hopfield neural network and a class of switch nonlinear system.
The main results obtained in this paper are as follows:
1. Stochastic robust stability problem for a class of Hopfield neural
network systems with delays and Markovian jumping parameters is
discussed. Base on the Lyapunov-Krasovskii functional approach and
stochastic analysis approaches, some stability conditions are presented,
which can be expressed in terms of linear matrix inequalities.
2. Stability and H ∞ control problem for a class of Hopfield neural
network systems with delays and Markovian jumping parameters is
discussed. Base on the Lyapunov-Krasovskii functional approach and
stochastic analysis approaches, a delay-dependent stability criterion is
obtained by linear matrix inequalities. Furthermore, corresponding H ∞
control laws are given.
3. The stability and H ∞ control problem for a class of uncertain
switch nonlinear systems is discussed. Base on the Lyapunov-Krasov
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