Discrete-time controller design for multivariable systems via engineering performance indices

This paper is devoted to linear multivariable controlled plants subjected to unknown bounded external disturbances. We propose a method for designing discrete-time output feedback controllers ensuring desired or achievable performance indices: accuracy, settling time, and stability margins for each control loop at the plant’s input. The controller design approach is based on the standard $H_\infty$ optimization procedure formulated in a particular way. Robust properties of the systems designed are investigated using the Nyquist plots of separate open control loops with break points at the plant’s inputs. The absolute stability of the closed-loop system with sectoral nonlinearities at the plant’s inputs and a relation with the radius of stability margins are proved. A numerical example is provided to demonstrate the effectiveness of this approach.