Dynamics Of Unstable Linear Systems Under Unbalanced Delta-Modulated Feedback Control

This paper addresses dynamics of unstable linear discrete-time systems under unbalanced delta-modulated feedback control. Firstly, the discrete-time systems is introduced in detail. We mainly research one-dimensional discrete-time systems with a parameter a > 1. For one-dimensional discrete-time systems with a parameter a > 1, we discuss and prove the basic properties of a system of Type I. So, we show that a system of Type I has a f _a- invariant interval, and it has two attractive regions. Dynamics of a system of Type I are mainly considered in the f_ a- invariant interval. Moreover, several special periodic motions of a system of Type I are classified and discussed, and we show that periodic motion of a system of TypeⅠis related to unbalancedΔ-modulation rateγand system parameter a .Secondly, we study the basic properties of a system of Type II with a parameter a < -1 . The researches have shown that a system of Type II has a f a? invariant interval, and it has two attractive regions. Dynamics of a system of Type II are mainly considered in the f a? invariant interval. Several special periodic motions of a system of Type II are classified and discussed, and we show that different relations of unbalancedΔ-modulation rateγrelative to system parameter a will determine different periodic motions of a system of TypeⅡ.Finally, in the second and third part end, through the matlab experiment, we mainly research both derived second and third order quantized feedback control systems. The researches have shown different distribution of strange attractors.