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Global stabilization of uncertain lotka-volterra systems via positive nonlinear state feedback

Badri, V ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2020.2972832
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2020
  4. Abstract:
  5. This article deals with stabilization of Lotka-Volterra (LV) systems in the presence of interval uncertainty and a physical limitation on the control input, which restricts this input to be strictly positive. Considering the positiveness property of LV systems, a quasi-monomial structure for the state feedback based control input is proposed. Considering this structure, stability of the closed-loop system with no uncertainty is analyzed. This analysis leads to an algebraic inequality, whose satisfaction guarantees stability of the closed-loop system. To extend this result to uncertain LV systems with interval parameter uncertainty, a new approach, by which stability of the positive equilibrium point of the closed-loop uncertain LV systems can be checked in terms of feasibility of a component-wise linear matrix inequality (LMI), is introduced. To achieve a stabilizing controller, the unknown controller parameters are obtained by using the feasible solutions of the mentioned LMI. To overcome some restrictions on the proposed method, a new Lyapunov function is employed, which leads to a bilinear matrix inequalities (BMI) to ensure stabilization. This BMI approach reduces the conservativeness of the above-mentioned LMI-based approach. Also, it is shown that the BMI-based approach can be extended for global stabilization of time-varying LV systems. The efficiency of the proposed schemes is shown through some examples inspired from chemical/biological processes. © 1963-2012 IEEE
  6. Keywords:
  7. Biological network ; interval uncertainty ; Lotka-Volterra (LV) system ; nonlinear state feedback ; positive control ; stabilization ; Controllers ; Linear matrix inequalities ; Lyapunov functions ; Nonlinear feedback ; Stabilization ; State feedback ; System stability ; Uncertainty analysis ; Bilinear Matrix Inequality(BMI) ; Controller parameter ; Feedback-based control ; Global stabilization ; Interval uncertainty ; Lotka-Volterra systems ; Nonlinear state feedbacks ; Stabilizing controllers ; Closed loop systems
  8. Source: IEEE Transactions on Automatic Control ; Volume 65, Issue 12 , 2020 , Pages 5450-5455
  9. URL: https://ieeexplore.ieee.org/document/8988207