Time-triggered control of nonlinear discrete-time systems

We investigate the time-triggered control of nonlinear discrete-time systems using an emulation approach. We assume that we know a controller, which stabilizes the origin of a discrete-time nonlinear system. We then provide conditions to preserve stability when the control input is no longer updated at each step, but within N steps from the previous update, where N is a strictly positive integer. We consider general output feedback controllers and we allow for various holding strategies of the control input between two updates, such as zero-input or hold-input policies for example. An easily computable bound on the maximum number of steps between two updates, N, is provided. The results are applied to linear time-invariant systems in which case the assumptions are written as a linear matrix inequality, and a nonlinear physical example is provided as an illustration. This study is relevant for networked control systems, as well as any system for which sparse or sporadically changing control inputs are advisable in view of the resource limitations for instance.