Dwell-Time-Based Robust Stabilization and $L_{2}-$ Gain Analysis for Asynchronously Switched Linear Systems With Actuator Saturation

This paper studies the robust stabilization problem and
$L_{2}-$
gain analysis for a class of asynchronously switched linear systems with actuator saturation under the dwell time switching signal. The switching signal of the switched controller involves time delay, which results in the asynchronous switching between the candidate controller and the subsystems. The matched state feedback controllers for each subsystem are designed by proposing a new type of multiple time-varying piecewise Lyapunov functions (MTVPLFs), and the computable sufficient conditions for the robust stabilization and
$L_{2}-$
gain problem of the studied switched systems are proposed respectively within the framework of a dwell-time switching. The convex hull technique is employed to deal with actuator saturation. Finally, an illustrative example of the problem of the continuously stirred tank reactor is presented to demonstrate the effectiveness of our proposed method.
Note to Practitioners
—In asynchronously switched linear systems with actuator saturation, the stability of the systems is very important. Actuator saturation is one of the reasons for degrading system performance, and the switching instants of the controllers may lag behind the corresponding subsystems to generate asynchronous switching. The coexistence of actuator saturation and asynchronous switching exacerbates the instability of the switched systems. In view of actuator saturation and asynchronous switching, the asynchronous state feedback controllers for each subsystem are designed by proposing a new type of MTVPLFs and dwell time switching strategy.