Stabilization of Uncertain Discrete-Time Linear System With Limited Communication

TLDR: It is shown that the robust control law with aperiodic information ensures input-to-state stability of the original system in the presence of mismatched uncertainty, and derived the event-triggering condition for a discrete-time uncertain system.

Abstract: This technical note proposes a procedure to control an uncertain discrete-time networked system using an aperiodic stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. Aperiodic exchange of information is done due to bandwidth constraint of the communication network. An event-triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks. In event-triggered control, the control input is computed and actuated 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. It is shown that the robust control law with aperiodic information ensures input-to-state stability (ISS) of the original system in the presence of mismatched uncertainty. Deriving the event-triggering condition for a discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one.