Clarification of Free Parameters of State-dependent Coefficient Form: Effect on Solving State-dependent Riccati Inequality

Abstract

Recently, nonlinear H∞ control theory has been paid attention for the powerful design method for a robust stabilization. The solvable condition of nonlinear H∞ control problem is given by the Hamilton Jacobi Inequality (HJI). The HJI is the partial differential inequality which is quite difficult to solve, so some numerical approaches have been researched.The approach to solve the HJI based on State-dependent Riccati Inequality (SDRI) is proposed. The SDRI is derived from the HJI with a State-dependent Coefficient form (SDC form) of a nonlinear system under an integrability constraint. Here, since the SDC form for a nonlinear system is not unique, free parameters of the SDC form can be considered.In this paper, a new expression of free parameters to completely express the SDC form is proposed. Using free parameters, a desirable numerical solution of the SDRI can be calculated. We focus on a constant solution of the SDRI because the integrability constraint can be neglected. Finally, numerical examples to verify the advantage of the free parameters of SDC form are given.