Abstract
This work is devoted to solving synchronization problem of uncertain chaotic systems with dead zones. Based on the Lyapunov stability theorems, by using fuzzy inference to estimate system uncertainties and by designing effective fuzzy adaptive controllers, the synchronization between two chaotic systems with dead zones is realized and a fuzzy variable-structure control is implemented. The stability is proven strictly, and all the states and signals are bounded in the closed-loop system. A simulation example is presented to test the theoretical results finally.
Highlights
It is widely known that chaos is almost everywhere in the domain of engineering and science. It is a kind of complex dynamic behavior of nonlinear dynamic systems, and chaos has many applications in mechanical, electronics, and biochemistry fields. ere are many common chaotic systems, such as Chen system [1, 2], Lorenz system [3], Genesio–Tesi system [4, 5], Rossler system [6], and Lur’e system [7]
Ey found that if the chaotic system can be decomposed into two subsystems, and, in the response system, all the conditional Lyapunov exponents are less than zero, there will be chaotic synchronization effect in the drive and response system [1, 12]
For two chaotic systems starting from different initial points, their trajectories gradually tend to be consistent with each other over time, and this synchronization is structurally stable [13,14,15]
Summary
It is widely known that chaos is almost everywhere in the domain of engineering and science. Please refer to [15, 24,25,26,27,28,29,30] for some works about synchronization study in chaotic dynamical systems, which are subject to input nonlinearity.
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