Analysis and Design of Digital Chaotic Systems With Desirable Performance via Feedback Control

The dynamical degradation of digital chaotic systems (DCSs) often has serious negative influences on some digital chaos-based systems and then becomes one of the bottleneck problems stopping chaos from some applications. In this paper, we first restrict the Devaney's chaos definition to finite state sets to describe the chaotic motion of digital systems. Then, we propose a novel control method for DCSs based on the differential mean value theorem and state feedback technology. Simulation results show the effectiveness, robustness, and superiority of the proposed method. Finally, we construct a new pseudorandom number generator (PRNG) and evaluate its randomness via NIST SP800-22 and TestU01 test suites. Statistical test results show that the proposed PRNG has high reliability of randomness, thus it can be used for cryptography and other potential applications.