Parametric Quadratic Stabilization of a Class of Discrete-Time Uncertain Nonlinear Systems

The existence, uniqueness, and stability of equilibrium points in nonlinear systems are often challenged by parameter variations, which can limit the effectiveness of conventional stability analysis methods. This paper addresses the parametric quadratic stabilization of discrete-time uncertain nonlinear systems with parameter-dependent coefficients and sector-bounded nonlinearities. A linear state feedback control law is designed, and a parameter-dependent linear matrix inequality (LMI) condition is derived to guarantee the existence, uniqueness, and quadratic stability of a closed-loop equilibrium point. To handle parameter uncertainties, a sequential randomized algorithm is applied, yielding a probabilistic solution that ensures parametric quadratic stabilization with high confidence.