Exponential stabilization of continuous-time dynamical systems via time and event triggered aperiodic intermittent control

Abstract

This paper studies the exponential stabilization of continuous-time dynamical systems via aperiodic intermittent controls (APIC). Time-triggered and event-triggered APIC schemes are designed respectively for continuous-time dynamical systems. Under time-triggered APIC (T-APIC), by proposing the notions of (minimum) average control width and using the method of Lyapunov-like function, the exponential stabilization criteria expressed by converse average dwell-time conditions are derived. Based on indices of threshold-value and check-period, the event-triggered APIC (E-APIC) is proposed. E-APIC is state dependent and the algorithm for E-APIC is given to derive criteria of exponential stabilization. Moreover, by introducing control-free index into APIC, an E-APIC with state-based control widths (SCW) is proposed to improve the constraints on control widths in E-APIC and T-APIC. In order to verify performances of the intermittent control schemes including periodic intermittent control (PIC), some discussions are given by using notions of number of control, rate of control, and cost of control. Finally, one example with numerical simulations is given for illustrations. It is shown that both PIC and T-APIC are stronger control schemes than E-APIC and E-APIC with SCW. E-APIC and E-APIC with SCW have better performances than PIC and T-APIC with lower values on rate of control, number of control, and cost of control. And E-APIC with SCW has lowest rate of control and can achieve least total control time.