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

Highlights：

• Two kinds of aperiodic intermittent control (APIC) schemes, i.e., time-triggered APIC and event-triggered APIC, are proposed respectively for continuous-time dynamical systems (CDS).

• By proposing the notions of (minimum) average control width and using the method of average dwell-time (ADT) including converse ADT, the exponential stabilization criteria are derived for CDS under time-triggered APIC (T-APIC).

• Based on two levels of event conditions via indices of threshold-value and check-period, the event-triggered APIC (E-APIC) is constructed for CDS. E-APIC is state dependent and in E-APIC, by replacing to test the converse average dwell-time conditions in T-APIC, the algorithm for E-APIC is given to derive criteria of exponential stabilization of CDS.

• 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 control schemes including periodic intermittent control (PIC), T-APIC, E-APIC, and E-APIC with SCW, the notions and discussions of number of control, rate of control, and cost of control are given.

• 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 EAPIC 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.