Mixed continuous-time and discrete-time ℋ∞ control

A Riccati equation (RE) based solution to the ℋ_∞ optimal control problem for mixed continuous-time and discrete time systems is presented. The results unifies a number of recently penetrated H_∞ control problems. A general criterion (D ₁₁≠0) is handled without any sophisticated transformations; only the simple transformation from LQ-theory which removes the “cross-penalty” term is applied. In the infinite-horizon case a periodic behavior is assumed, and it is shown how the related continuous RE can be replaced by an equivalent discrete one. It is also shown how an algebraic RE which involves the system behavior during one period can be formulated and solved applying standard techniques