Treatment of Restriction Condition of Discrete _(H_∞) Model-matching Problem

摘要

The _(H_∞) model-matching problem of discrete-time systems was solved by using conjugation method in this paper. The restriction that _(T_2~(-1)(z)) and _(T_3~(-1)(z)) must be anti-stable is required before, we can decompose the A matrices of _(T_2~(-1)(z)) and _(T_3~(-1)(z)) into stable and unstable portions, then this restriction can be removed with some similar transformations and matrix operations. So the simpler result and calculation algorithm of _(H_∞) model-matching problem of discrete-time systems can be given according this method. Only eigenvalue problem and Lyapunov equation need to be solved instead of solving Riccati equations and some complex decomposition problems. The result given here is proved and can be programmed with software and used to solve more general _(H_∞) model-matching problem of discrete-time systems.