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This work applies the LQ control framework to the class of quasi-polynomial and Lotka-Volterra systems through the linearized version of their nonlinear system model. The primary aim is to globally stabilize the original system with a suboptimal LQ state feedback by means of a well-known entropy-like Lyapunov function that is related to the diagonal stability of linear systems. This aim can only be reached in the case when the quasi-monomial composition matrix is invertible. In the rank-deficient case only the local stabilization of the system is possible with an LQ controller that is designed using the locally linearized model of the closed-loop system model.

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LQ Control of Lotka-Volterra Systems Based on their Locally Linearized Dynamics**This research is supported by the National Research, Development and Innovation Office - NKFIH through grant No. 115694, ***A. Magyar was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences