Hybrid Control of ADT Switched Linear Systems subject to Actuator Saturation

TL;DR

This paper introduces a hybrid output-feedback control method for ADT switched linear systems with actuator saturation, ensuring stability and disturbance attenuation through LMIs and a reset mechanism.

Contribution

It develops a unified convex synthesis framework incorporating reset rules for switched systems with saturation, addressing stability and performance simultaneously.

Findings

Guarantees exponential stability under ADT switching.

Achieves prescribed ${\ m L}_2$-gain disturbance attenuation.

Demonstrates effectiveness through simulations and computational efficiency.

Abstract

This paper develops a hybrid output-feedback control framework for average dwell-time (ADT) switched linear systems subject to actuator saturation. The considered subsystems may be exponentially unstable, and the saturation nonlinearity is explicitly handled through a deadzone-based representation. The proposed hybrid controller combines mode-dependent full-order dynamic output-feedback controllers with a supervisory reset mechanism that updates controller states at switching instants. By incorporating the reset rule directly into the synthesis conditions, switching boundary constraints and performance requirements are addressed in a unified convex formulation. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee exponential stability under ADT switching and a prescribed weighted ${\cal L}_2$-gain disturbance attenuation level for energy-bounded disturbances. An explicit controller construction algorithm is provided based on feasible LMI solutions. Simulation results demonstrate the effectiveness and computational tractability of the proposed approach and highlight its advantages over existing output-feedback saturation control methods.