Analytical representation of the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable systems

Recently, the easy-to-implement state-dependent Riccati equation (SDRE) strategy has been shown effective for numerous practical applications. Since being similar to SDRE, the newly emerged state-dependent differential Riccati equation (SDDRE) approach shares most of the benefits of SDRE, and exhibits interesting potential from both the analytical and practical viewpoints. By generalizing previous works to the general-order nonlinear time-variant systems, we try to resolve several problems related to the design flexibility (the infinitely many candidates of the state-dependent coefficient matrix), since they appear at the beginning of the implementation of both schemes. Finally, we demonstrate the proposed scheme via examples.