Design of Free Parameters of State-Dependent Coefficient Form Based on the Relation between State-Dependent Riccati Inequality and Hamilton Jacobi Inequality

Abstract

The solvable condition of nonlinear H ∞ control problems is given by the Hamilton Jacobi inequality (HJI). The state-dependent Riccati inequality (SDRI) is one of the approaches used to solve the HJI. The SDRI contains the state-dependent coefficient (SDC) form of a nonlinear system. The SDC form is not unique. If a poor SDC form is chosen, then there is no solution for the SDRI. In other words, there exist free parameters of the SDC form that affect the solvability of the SDRI. This study focuses on the free parameters of the SDC form. First, a representation of the free parameters of the SDC form is introduced. The solvability of an SDRI is a sufficient condition for that of the related HJI, and the free parameters affect the conservativeness of the SDRI approach. In addition, a new method for designing the free parameters that reduces the conservativeness of the SDRI approach is introduced. Finally, numerical examples to verify the effect of this method are presented.

A Bilinear H∞ Controller Using a Bilinear Disturbance Isolation Observer for a Heat Exchanger Containing Unknown Disturbance Flows

“…ΔY sub (u,x) := Y(u,x) (18) where Y(u(t),x(t)) is a symmetric positive definite matrix given in the next theorem, β and λ are appropriate positive numbers.…”