Robust H∞ n-D feedback control system

A n-D polynomial solution is proposed for an optimization of linear SISO n-D control problems. The method optimizes an Hⁿ cost function that contains the model uncertainty disturbance attenuation and rejection and power limitation. These are expressed in terms of required bounds of the sensitivity function and its complement. The approach of the paper leads to formulation of n-D control systems into a performance n-D polynomial equation. This type of problem is mainly found in distributed-parameter systems, time delay systems, decentralized control, and the like. The polynomial solution yields the desired n-D controller that optimizes the suggested cost function. The polynomial approach is preferred here due to the simplicity of plant representation and the wealth in frequency domain properties of polynomial algebra. The setting of the problem is on the ring P[z₁ , ..., z_a], the plant operator function belongs to the rational field of R(z₁, ..., z_c) and the controller which optimizes the performance as well belongs to the rational field R(z₁, ..., z_n)