The robustness of the stabilizing regulator for quasi-linear discrete systems with state dependent coefficients

This paper deals with the construction of a nonlinear stabilizing regulator based on a D-SDRE (Discrete-Time State Dependent Riccati Equation) technique for a class of nonlinear discrete-time control systems which can be transformed to quasi-linear form by the formal extraction of a small parameter. The scheme for the proof of the stability of the closed-loop system has been included, it is carried out along the line of the Lyapunov formalism. The proposed regulator design algorithm significantly reduces computational costs and helps to find a suboptimal regulator in terms of the constructed cost function. Moreover the robustness to parametric uncertainties of the closed-loop quasi-linear system along the constructed nonlinear regulator has been examined. The asymptotic stability and robustness of the closed-loop system is demonstrated on the example of an inverted pendulum discrete model.