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.