Constrained ℋ∞ optimal control in sampled data systems

The problem of minimizing the closed-loop L₂ gain between inputs w_f and outputs z_f while some closed loop responses z_t due to test inputs w_t satisfy given constraints is considered and solved for sampled data systems. Based on results given by Bamieh et al. (1992), this problem is reduced exactly to a constrained ℋ_∞ optimization problem for a discrete time plant which can solved by the algorithm of Sideris et al. (1993, 1994). Time domain constraints in between sampling instances can be reflected without approximation to the problem variables defined on the sampling times. In comparison with an approximate solution obtained by first discretizing the continuous time plant and then applying the results of Sideris et al., the variables and the constraints of the finite dimensional optimization problem involved in the solution can be drastically reduced