Optimal Ultimate Bound of Synchronized Multi-Agent Systems with Quantized Control Inputs: An Input-to-State Stability Approach
Victor Daniel Reyes Dreke, Zhiyong Sun, Mircea Lazar · 2025
Multi-agent systems (MASs) are commonly found in applications where guaranteeing stability and performance is crucial. However, due to the limited actuator resolution and communication bandwidths, their control inputs tend to have a quantized behavior that can affect their closed-loop performance. This paper studies the output synchronization of homogenous MAS with general linear dynamics under quantized control input. We propose a method for designing distributed output feedback controllers that minimizes the synchronization error. To do this, we formulate a linear matrix inequality (LMI) using the input-to-state stability (ISS) framework to compute the ultimate bound of the synchronization error. Moreover, we leverage the proposed LMI in an optimization problem to synthesize a distributed controller, i.e., feedback gain, that minimizes this synchronization error bound. Due to the proposed controller structure, we can use a linear search algorithm that guarantees finding less conservative and optimal bounds. A simulated example of synchronizing a platoon of vehicles demonstrates the effectiveness of our method.