A Unified Lorenz-Like System and Its Tracking Control* *Supported by the Research Foundation of Education Bureau of Hunan Province of China under Grant No. 13C372, Jiangsu Provincial Natural Science Foundation of China under Grant No. 14KJB120007 and the Outstanding Doctoral Dissertation Project of Special Funds under Grant No. 27122

Abstract

This paper introduces the finding of a unified Lorenz-like system. By gradually tuning the only parameter d, the reported system belongs to Lorenz-type system in the sense defined by Člikovský. Meanwhile, this system belongs to Lorenz-type system, Lü-type system, Chen-type system with d less than, equivalent to and greater than 1.5, respectively, according to the classification defined by Yang. However, this system can only generate a succession of Lorenz-like attractors. Some basic dynamical properties of the system are investigated theoretically and numerically. Moreover, the tracking control of the system with exponential convergence rate is studied. Theoretical analysis and computer simulation show that the proposed scheme can allow us to drive the output variable x1 to arbitrary reference signals exponentially, and the guaranteed exponential convergence rate can be estimated accurately.