Lyapunov’s stability analysis for first degree polynomial systems, subject to risk-sensitive control

• Published in: Mathematics and computers in simulation Vol. 226; pp. 464 - 473
• Main Authors: Hernandez-Castorena, Gerardo Armando, Alcorta-Garcia, Maria Aracelia, Saenz-Esqueda, Jose Armando, Mendez, Gerardo Maximiliano
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2024
• Subjects: Lyapunov’s analysis; Nonlinear polynomial systems; Robustness of the solution; RS controllers; Lyapunov’s analysis; RS controllers; Robustness of the solution; Nonlinear polynomial systems
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2024.07.006

This work presents a novel methodology to verify the stability of first-degree stochastic polynomial systems under a Risk-Sensitive (RS) optimal control using Lyapunov’s stability analysis theory. The so-called Lyapunov’s indirect method is applied to prove its stability when it is combined with the dynamics of Riccati’s gain equation. The proposed methodology guarantees both the exponential stability of deterministic systems and the robustness of stochastic systems. Simulation results demonstrate the robustness, the effectiveness and the feasibility of this proposal. •Stability for deterministic non linear systems and RS optimal control applying Lyapunov theory.•Stability for stochastic non linear systems and RS optimal control applying Lyapunov theory.•Application and validation of results.