Stabilization of Uncertain Discrete-time Linear System via Limited Information

TL;DR

This paper develops an event-triggered robust control method for uncertain discrete-time systems with limited communication, ensuring stability despite network unreliability and parametric uncertainties.

Contribution

It introduces a novel event-triggering condition and control strategy that guarantees input-to-state stability for uncertain systems with limited information.

Findings

The proposed control law stabilizes uncertain systems under limited communication.

Event-triggered control reduces communication load compared to periodic updates.

Numerical example demonstrates improved performance over traditional methods.

Abstract

This paper proposes a procedure to control an uncertain discrete-time networked control system through a limited stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. The input information is limited due to unreliability of communicating networks. An event-triggered based robust control strategy is adopted to capture the network unreliability. In event-triggered control the control input is computed and updated at the system end only when a pre-specified event condition is violated. The robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost-functional. The designed robust control law with limited information ensures input-to-sate stability (ISS) of original system under presence of mismatched uncertainty. Deriving the event-triggering condition for discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this paper. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one.