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

TL;DR

This paper develops a stochastic system model for analyzing the stability and $ive$ performance of linear networked and quantized control systems affected by delays and packet losses, providing new stability conditions.

Contribution

It introduces a novel stochastic modeling approach and establishes sufficient stability and performance conditions for networked control systems with uncertainties.

Findings

Derived stability conditions for networked control systems.

Demonstrated $ive$ performance guarantees under network uncertainties.

Validated results with a numerical example.

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.