Output feedback stabilization of logical dynamical systems with state‐dependent control constraints

Abstract

AbstractControl constraints are common in real‐world applications. However, when the control constraint depends on the system state, designing a stabilizing output feedback that adheres to the constraint can be challenging if the state is unmeasurable. This study proposes a novel dual‐loop structural output feedback for logical dynamical systems (LDSs) with state‐dependent control constraints. The inner‐loop controller is a pre‐output feedback designed based on the state‐dependent constraint, which always selects a common admissible control for all possible states. A system with free control input is obtained by combining the pre‐output feedback with the LDS. The outer‐loop controller, an ordinary output feedback, is then designed for the combined system. It is proven that any admissible time‐invariant output feedback can be decomposed into a pre‐output feedback and an ordinary output feedback. Furthermore, a necessary and sufficient condition for stabilizability by admissible output feedback is obtained. Finally, an example is presented to demonstrate the effectiveness of the obtained results.