Global Exponential Stability for Discrete-Time Nonlinear Systems Using SDC Parametrization

Since the mid-1990s, State-Dependent Riccati Equation (SDRE) strategies have gained prominence as systematic and effective methodologies for designing nonlinear controllers, observers, and filters. These approaches address many of the limitations inherent in traditional techniques while offering computationally efficient algorithms that have demonstrated remarkable success across a wide range of practical and impactful applications. In this letter, we leverage the State-Dependent-Coefficient (SDC) parametrization to establish a novel global asymptotic (and exponential) stability result for discrete-time nonlinear systems with a controllable SDC representation. The proof is based on geometrical tools and spectral decompositions. Numerical simulations validate the results.