Stability of Periodic Movements in Sampled Data Relay Feedback Control Systems

Well-known methods for identification symmetric periodic motions and assess their stability in continuous relay feedback control systems. Time discretization can lead to the emergence of many available symmetrical periodic motions. In a sampled-data relay control systems (RCS) there may be microchaotic oscillation. In this paper we propose a criterion to evaluate the stability of such movements. Self-oscillating RCS operating in discrete time are considered. Using the method of a discrete locus of a relay system all possible symmetrical periodic motions in an autonomous discrete relay system are identified. Next, the stability of the limit cycle with the maximum possible repetition period is evaluated. The method of analysis of global asymptotic stability of periodic motions developed for a continuous RCS, for a class of discrete systems is used. The developed method is based on the use of the Lyapunov function and the theory of linear matrix inequalities (LMI).