Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking problem. These solutions are based on proposed stabilizing gains solving a pole placement problem by output feedback. The proposed gains simplify the coprime factorizations of the plant and the controller, and allow assigning a decoupled characteristic polynomial. The 2DOF stabilizing control is based on the Parameterization of All Stabilizing Controllers (PASC) where the free parameter in the feedback part of the controller solves the mixed sensitivity robust control problem of attenuation of a Low-Frequency (LF) additive disturbance at the input of the plant and of a High-Frequency (HF) additive disturbance at the measurement, while the free parameter in the reference part of the controller assures that the controlled output tracks the reference at LF such as step or sinusoidal inputs. With the proposed expressions, the mixed sensitivity problem is solved without using weighting functions, so the controller does not increase its order; and the infinite norm of the mixed sensitivity criterion, as well as the assignment of poles, is determined by a set of control parameters.
The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or H2 criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or H2 quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure the designer could use controller with different structures such as P, PI, PID, PI-D. For the PI-D's D-part of controller feedback the designer could choose any available output/state derivative variables of descriptor systems. Obtained design procedure is in the form of Bilinear Matrix Inequality (BMI). The effectiveness of the obtained results is demonstrated on two examples.