Bumpless transfer proportional-integral-derivative control of switched positive systems

This paper addresses the bumpless transfer proportional-integral-derivative (PID) control for discrete-time switched systems with average dwell time (ADT). First, a bumpless transfer performance is proposed to reduce the control bumps caused by switching of the systems. Then, a PID controller is constructed to achieve the positivity and stability under synchronous switching. Under the PID control, the system is transformed into a time-delayed system. Sufficient conditions are derived to preserve the positivity, stability, and bumpless transfer performance. Moreover, a PID controller is proposed under the asynchronous switching case. All gain matrices of the PID controller are described via a matrix decomposition approach. Using the copositive Lyapunov function and linear programming, the positivity, stability, and bumpless transfer performance of the system are achieved under synchronous and asynchronous switching cases, respectively. Finally, two examples are provided to illustrate the effectiveness of the proposed approaches.