The L∞/L2‐Gain Analysis for Periodic Event‐Triggered Control Systems: Discretization Approach and Convergence Rate Analysis

This paper is concerned with the ‐gain (i.e., the gain from to ) analysis of periodic event‐triggered control (PETC) systems, where the feedback loop between a continuous‐time plant and a discrete‐time controller is activated intermittently based on a periodic event‐triggering mechanism. To take into account the hybrid continuous/discrete‐time behavior of PETC systems, their operator‐based description is first established by using the continuous‐time lifting technique. To facilitate the ‐gain analysis for PETC systems, we derive their fast‐lifted representation by dividing the sampling interval into subintervals with an equal width. This allows us to develop an approach by which the output function on each subinterval is approximated by a constant function. The proposed PCA approach converts a PETC system into a discrete‐time event‐triggered control (ETC) system, whose ‐gains are shown to converge to the ‐gains of the original PETC system in the order of , where is the PCA parameter. On the basis of the convergence property, the ‐gain of PETC systems is further characterized in terms of some linear matrix inequalities (LMIs). Finally, a numerical example is given to verify the effectiveness of the arguments developed in this paper.