Abstract
The design and application of state estimator for a class of time-delay systems with state saturation nonlinearities are firstly explored. Based on the Lyapunov-Razumikhin functions, delay-dependent sufficient conditions are established to guarantee the asymptotic stability of the error between the state estimate and the true state. Besides, an upper bound of arbitrary time-varying delays is derived to assure that the resulting error can converge asymptotically to zero. Finally, applications to the secure communication and simulation results are given to demonstrate the feasibility and effectiveness of the main results.
Highlights
It is well known that time delays are frequently encountered in various physical dynamic systems and may lead to instability or oscillation
Time-delay systems have been extensively studied; see, for instance, [1,2,3,4,5,6,7,8], and they are often encountered in various areas, such as chemical engineering systems, electrical system, mechanical system, biological system, transportation system, the nuclear reactor, AIDS epidemic, and systems with lossless transmission lines
The Lyapunov-Krasovskii approach controller design and stability analysis are more complex than the LyapunovRazumikhin approach
Summary
It is well known that time delays are frequently encountered in various physical dynamic systems and may lead to instability or oscillation. The Lyapunov-Krasovskii approach frequently requires the time-varying delay hi(t) to meet some conservational conditions such that hi(t) is bounded and ḣi(t) ≤ 1 but the Lyapunov-Razumikhin approach only requires the time-varying delay to be bounded. To the author’s knowledge, there have not been any reported results on the use of the Lyapunov-Razumikhin method for state estimator of time-delay systems with state saturation nonlinearities. It is important to develop a novel state estimate for a class of time-delay systems with state saturation nonlinearities and time-varying delays via the Lyapunov-Razumikhin technique. Mathematical Problems in Engineering state saturation nonlinearities and time-varying delays; (III) calculating an upper bound of arbitrary time-varying delays without destroying the state estimator; (IV) constructing an observer-based secure communication architecture to demonstrate the practicability and effectiveness of the main results
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