H∞ Control of Nonlinear DC Motor Systems: One-Sided Lipschitz Approach *

In this study, we explore the problem of achieving <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> ∞ control for a specific type of nonlinear systems characterized by one-sided Lipschitz (OSL). Initially, we introduce a model for a nonlinear DC motor. Subsequently, we employ a technique that separates the Lyapunov matrix from the system matrix to establish less conservative conditions for analysis. Following this, we determine the control gain using a decoupling approach technique based on Linear Matrix Inequalities (LMIs), ensuring both asymptotic stability and effective suppression of disturbances in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> ∞ sense. Finally, the proposed approach is validated through simulations demonstrating the controlled behavior of the nonlinear DC motor system.