X-factorable transformation-based control of interconnected Lotka-Volterra systems

A dynamic model of interconnected Lotka-Volterra systems has been developed both with static and delayed interconnections. We have shown that the X-transformed model of interconnected Lotka-Volterra systems naturally admits a quasi-polynomial (QP) representation, facilitating systematic analysis and control design. In order to analyze local asymptotic stability around a positive equilibrium, we have shown that the X-factorable transformation preserves local diagonal stability. We propose a decentralized setpoint-tracking controller design based on the transformed model that guarantees population persistence in the subsystems of the network. The proposed controller design is computationally simple and ensures that the controlled system is locally diagonally stable around the prescribed setpoint. Moreover, larger controller gains improve disturbance attenuation, mitigating the effect of the disturbance offset term on control performance.