Determination criterion of finite escape phenomena of H∞-differential Riccati equations

The paper presents a criterion and the corresponding algorithm for the determination of finite escape phenomena of H-infinity-differential Riccati equations. For finite horizon H-infinity control or filtering problem, the existence of solution of the associated H-infinity-differential Riccati equation with arbitrary positive initial condition depends on the induced norm of the system, and the worst-case induced norm gamma(cr) is a critical value for the existence of the solution. According to the analogy between structural mechanics and optimal control, the parameter gamma(cr)(-2) that guarantees the existence of positive, continuous and differentiable solutions to the H-infinity-differential Riccati equations is also the fundamental eigenvalue of a generalized Rayleigh quotient. Therefore, this parameter can be computed precisely with the precise integration method and extended Wittrick-Williams algorithm, which is an effective algorithm for the computation of eigenvalues of the generalized Rayleigh quotient.