Stabilization of Nonlinear Parameter Varying Systems Using LMIs: An Observer-Based Controller Framework

This paper investigates the observer-based stabilization problem for a class of disturbance-affected Nonlinear Parameter-Varying (NLPV) systems. We introduce a novel observer-controller framework that leverages Linear Matrix Inequality (LMI) conditions to guarantee robust performance. Unlike previous works that focus solely on state estimation, our approach integrates a controller based on the estimated states to ensure asymptotic stability and optimal disturbance attenuation. Through the deployment of the parameter-dependent Lyapunov (PDL) function and H∞ criterion, a new LMI condition is synthesized to achieve the objective. Further, due to the judicious use of a variant of Young’s inequality, the reformulated Lipschitz property, and the matrix multiplier method presented in our previous works, the established LMI encompasses extra degrees of freedom from a feasibility point of view. The performance of the method is validated through simulations on a nonlinear time-varying pendulum system, demonstrating enhanced noise attenuation and faster convergence compared to existing approaches.