State-Space Solutions to H∞ Control Problems

In this chapter, we give a solution to the H∞ control problem in the state space based on the results obtained in the preceding chapters. A state-space realization of the plant (7.1) is given by8.1a$$\dot x = Ax + B_1 w + B_2 u,$$8.1b$$z = C_1 x + D_{11} w + D_{12} u,$$ 8.1c$$ y = C_2 x + D_{21} w + D_{22} u$$ where $$ z \in \text{ }R^m \text{ : errors to be reduced}, $$ $$ y \in R^q :\text{observation}\,\text{outputs}, $$ $$ w \in R^r :\text{exogenous}\,\text{inputs}, $$ $$ u \in R^p :\text{control}\,\text{inputs}. $$