An Analysis on Worst-case State Estimation in Standard H$\infty$ State-Space Solution

Worst-case state estimation will be proposed in this paper. By using the worst-case disturbance and worst-case state estimation, we can obtain right/left constrained coprime factors. If constrained coprime factors are used in designing a controller, the infinity-norm of closed-loop transfer matrix can be smaller than any constant .gamma.(> .gamma.$_{opt}$) without matrix dilation optimization. The derivation of left/right constrained coprime factors is achieved by doubly coprime factorization for the plant constrained by the infinity norm. And the parameterization of stabilizing controllers gives us easily understanding for H$_{\infty}$ control theory.ry.