Abstract
This paper presents the sum of squares (SOS)-based fuzzy control with H∞ performance for a synchronized chaos system and secure communications. To diminish the influence of the extrinsic perturbation, SOS-based stability criteria of the polynomial fuzzy system are derived by using the polynomial Lyapunov function. The perturbation decreasing achievement is indexed in a H∞ criterion. The submitted SOS-based stability criteria are more relaxed than the existing linear matrix inequality (LMI)-based stability criteria. The cryptography scheme based on an n-shift cipher is combined with synchronization for secure communications. Finally, numerical simulations illustrate the perturbation decay accomplishment of the submitted polynomial fuzzy compensator.
Highlights
In recent years, the studies on synchronization of chaos systems have acquired substantial attention
This paper proposes two novel theorems and the contributions of this article are summarized as follows
Using the property of a chaotic system, which is excessively reactive to original states, the chaos system can be applied to secure communications
Summary
The studies on synchronization of chaos systems have acquired substantial attention. This paper employs a polynomial Lyapunov function to acquire the sum of squares (SOS)-based stability criteria of chaotic synchronization systems to reduce the conservativeness of the LMI-based stability criteria. In [17], polynomial Lyapunov functions are designed by introducing a gradient algorithm without applying the typical transformation so that the polynomial fuzzy controller with SOS stability conditions was received. In [18], the message and character of membership functions are deliberated in the SOS-based stability design of (interval type 2) IT2 polynomial-fuzzy-model-based control systems. In [21], using the Lyapunov function and the S-procedure, SOS-based stability criteria are received for uncertain large-scale polynomial T–S fuzzy systems. Based on the above observations from the literature, this paper takes extrinsic perturbation into account to synthesize the H∞ control of polynomial fuzzy chaos synchronization systems.
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