Stability and ${\mathcal{H}}_{\infty }$ Performance Analysis of Stochastic Linear Networked and Quantized Control Systems

Abstract

This paper studies the stability and ${\mathcal{H}}_{\infty }$ performance analysis problem for linear networked and quantized control systems with both communication delays random packet losses. To deal with the network-induced uncertainties and random packet dropouts, a novel discrete-time stochastic system model is developed for continuous-time networked control systems, and further overapproximated via a polytopic system with norm-bounded uncertainty. Based on the overapproximated system model, sufficient conditions are established for linear networked and quantized control systems in different cases to guarantee input-to-state stability and ${\mathcal{H}}_{\infty }$ performance with respect to the network-induced errors. Finally, a numerical example is presented to illustrated the developed results.

8 pages, 2 figures, extended version of the ACC paper