On the stability of optimal controlled systems with SDRE approach

State Dependant Riccati Equation (SDRE) method is gaining more and more place as a promising emerged methodology for nonlinear control system design, and therefore becoming the basic theory about which are articulated many relevant recent approaches for the optimal control resolution of a control-affine nonlinear system. SDRE approach aims to solve a nonlinear optimal control problem through a Riccati equation that depends on the state. Our main contribution in this paper is to carry out the analysis of nonlinear systems associated with SDRE controllers aiming to determine new sufficient conditions for their stability.