Asynchronous control of networked periodic piecewise linear systems under time-varying transmission delay.

This paper studies the stability of networked periodic piecewise linear systems (NPPLSs) of which communication channels are subject to a time-varying transmission delay. Under data-sampling, the NPPLS is modeled as an asynchronous controlled periodic piecewise linear system with time-varying input delay, where the interval of asynchronous control in each subsystem is uncertain but bounded. Aimed at obtaining less conservative stability and synthesis results when tackling the uncertain switching, the dwell time of each subsystem is divided into three subintervals according to the asynchronous control interval and the maximum delay assumption. In this way, it allows the construction of piecewise Lyapunov functionals for one subsystem, the piecewise Lyapunov functionals capture different dynamic characteristics in each subinterval. Using this approach, general stability conditions of NPPLSs are derived. Then, by constructing Lyapunov functionals as a set of delay-dependent time-varying functionals, tractable exponential stability conditions of NPPLSs under transmission delay are developed using a scaling technique. Due to the coupling of the decision variables in the conditions, an iterative algorithm is proposed to solve the periodic controller gains. A numerical example is provided to illustrate the merits of the obtained controllers.