On Integral Input-to-State Stability Analysis for a Class of Switched Bilinear Control Systems

In this paper, the integral input-to-state stability (iISS) of switched bilinear systems is investigated, and the uniformly iISS with respect to some classes of switching laws is put forward and studied. By the stability indexes of subsystems and the weighting techniques, several criterions of iISS are presented, where the classes of switching laws are characterised by the stability indexes of two subsystem classes. Specially, the criterions of uniformly iISS are presented with respect to the class of switching laws classed by dynamic decay rate of system. It should be noted that besides reduces the threshold for subsystems to be identified as stable subsystems, a proper weight factor presents a bigger range of dynamic decay rate of stability such that a same decay rate only needs a smaller dwell time than the case without the weighting techniques.