17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper TuA05.1

Hespanha, Joao Pedro (Univ. of California, Santa Barbara), Teel, Andrew (Univ. of California, Santa Barbara)

Stochastic Impulsive Systems Driven by Renewal Processes

Scheduled for presentation during the Mini-Symposium "Computational Methods in Hybrid Systems" (TuA05), Tuesday, July 25, 2006, 10:25−10:50, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on June 23, 2024

Keywords Hybrid systems modelling, Networked control, Stability of stochastic systems

Abstract

Stochastic impulsive systems are defined by a diffusion process with jumps triggered by a renewal process, i.e., the intervals between jumps are independent and identically distributed. We construct a model for such systems based on jump-diffusion equations and provide Lyapunov-based conditions that guarantee their mean-square stability.

As an application, we show that stochastic impulsive systems can be used to model networked control systems with stochastic inter-sampling times and packet drops. Conditions for mean-square stability of the resulting systems are provided. For linear dynamics, these conditions can be formulated in terms of Linear Matrix Inequalities.

We use two benchmark examples that previously appeared in the literature to illustrate the use of our results and to investigate their conservativeness.