Feedback Control for Linear Systems with Disturbances and Input Constraints

Two features are frequently encountered in control practice: the necessity of satisfying input/state constraints and the presence of external disturbances. This paper proposes an approach to design a feedback controller for disturbance rejection without violating constraints. Robust invariant ellipsoid is introduced and a sufficient condition for it is presented for discrete-time linear systems with persistent bounded disturbance. Combining with input/state constraint handling, controller synthesis can be finally transformed to a linear matrix inequalities (LMIs) optimization problem. Moreover, we introduce the induced Leo-norm as the measurement of the performance of disturbance rejection and propose an algorithm to obtain its upper bound. The simulation example shows the effectiveness of the design method