Robust H∞ control of average dwell time switching systems via non-monotonic lyapunov function approach

This paper develops a non-monotonic Lyapunov function (LF) approach for discrete-time switching linear system with average dwell time (ADT) switching to improve the stability criterion and achieve better H
_∞
performance. Such an approach allows the LF to increase both at the switching instants and during the running time of subsystems, but guarantees an average decrease on every two sampling steps. Based on the results of stability and H
_∞
analysis, a robust H
_∞
controller is further designed. Moreover, the relationship between the time difference of LF and switching rate i.e. the ADT constraint, is revealed. An example is given to demonstrate the validity and potential of the developed results.