Stability of discrete-time delayed impulsive linear systems with application to multi-tracking

Abstract

This paper studies the stability issue for discrete-time delayed impulsive systems (DDIS). The DDIS model is formulated from a discrete-time delayed system with impulses. By using the matrix spectrum theory, the estimates of solution with growth exponent are derived for delayed difference inequalities. Based on these results, two types of criteria on exponential stability with an estimated convergence rate have been established for DDIS. The first type investigates the effect of destabilising impulses, while the second is for the case in which the impulses stabilise the unstable discrete-time delayed systems. As the application, the stability results are used to solve the multi-tracking issue for discrete-time dynamical networks by mixed impulsive networked control (MINC), in which the impulsive control signals are transmitted via a communication network. The effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed MINC. Finally, one example with numerical simulations is worked out for illustration.

Keywords:

• impulsive systems
• stability
• time-delay
• dynamical networks
• impulsive networked control
• tracking

Acknowledgements

The authors would like to thank the associate editor, Dr. Francoise Lamnabhi-Lagarrigue, and the anonymous referees for their helpful comments and suggestions.

Additional information

Funding

Research supported by the National Natural Science Foundation of China [grant number 61174075], [grant number 51177142) and the Hunan Provincial Natural Science Foundation of China [grant number 11JJ2038].