Stability and stabilization of linear impulsive systems with large impulse-delays: a stabilizing delay perspective. (English) Zbl 1461.93437
Summary: This paper deals with the stability and stabilization of linear impulsive systems with large impulse-delays. To explore the stabilizing effect of the time delay in the discrete-time dynamics, a switched impulsive system approach is developed to establish non-conservative stability criteria for linear impulsive systems with periodic impulses and constant delay. Subsequently, sufficient conditions are given for stability of the impulsive systems with aperiodic impulses and time-varying delay by quasi-periodic Lyapunov function methods. By exploiting the particular structure of the stability conditions, impulsive stabilization problem using artificial impulse-delay is further discussed. These results are applied to sampled-data systems with input delay. Compared with the well-known input-delay approach, the proposed switched impulsive system approach not only provides simple stability conditions but also captures the stabilizing effect of the delay. Two numerical examples illustrate the proposed theoretical results.
MSC:
| 93D23 | Exponential stability |
| 93C27 | Impulsive control/observation systems |
| 93C57 | Sampled-data control/observation systems |
| 93C43 | Delay control/observation systems |
| 93C05 | Linear systems in control theory |
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