Controller synthesis of multi dimensional, discrete LTI systems based on numerical solutions of linear matrix inequalities

To determine control parameters of single-input single-output (SISO) systems a lot of well known experimental, numerical and analytical methods are available. For example the method of Ziegler-Nichols is a well known approach to experimentally determine suitable control parameters for a PID control. For multiple-input multiple-output (MIMO) systems determination of attractive parameters are much more harder. For example, full state feedback can be used to solve the linear-quadratic regulator (LQR) problem and find such parameters. Nevertheless, not only solutions for full state feedback would be practical. This paper will present a new method to extract suitable parameters applicable to various control types. It is based on Lyapunovs' stability theory and uses the Schur complement to reformulate it into an optimization problem with linear matrix inequalities (LMI) as related constraints.