Decentralised state feedback design for large-scale linear systems subject to input saturation

This study considers the design of decentralised controllers for large-scale linear systems under actuator saturation. Saturation in the magnitude of the control input is first considered. For the closed-loop system under a saturating decentralised state feedback law, conditions are identified under which an ellipsoid is contractively invariant and thus within the domain of attraction, or the restricted L₂ gain from the disturbance to the output is less than or equal to a pre-specified value ??. Based on these conditions, the designs of decentralised state feedback laws that achieve large domains of attraction or low L₂ gains can be formulated as optimisation problems with bilinear matrix inequality (BMI) constraints. Numerical algorithms are developed to solve these BMI problems. These developments are also extended to the situation where the inputs are subject to nested saturation, such as simultaneous actuator magnitude and rate saturation. Throughout the study, numerical examples are used to demonstrate the effectiveness of the proposed design method.