Aperiodic intermittent control for discrete-time systems

In this manuscript, time-triggered and event-triggered aperiodic intermittent controls are proposed for asymptotic stabilization of unstable discrete-time systems. The time-triggered aperiodic intermittent controls (T-APICs) are designed respectively by imposing conditions on the average dwell-time and the minimum of the active control width. For event-triggered aperiodic intermittent controls (E-APICs), when the norm of the state violates the defined inequality, the control is triggered. For one proposed E-APIC mechanism, it is demanded that the control length should be bigger than a given constant. Then for another E-APIC mechanism, we impose a condition related to the state on the control length. By relaxing the constraints on the control gain matrix, the third E-APIC mechanism is proposed. For these control plans, the control continuously updates during the active control time interval. Then we propose another E-APIC for asymptotic stabilization of the discussed discrete-time system by using the concept of input -to-state stability (ISS) and imposing the conditions on the norm of the state. In order to exemplify the effectiveness of the proposed aperiodic intermittent control mechanisms, asymptotic stabilizations of three examples are discussed by the proposed theorems.