Reliable H∞ control for 2‐D discrete switched systems with state delays and actuator failures

Abstract

SummaryThis article is concerned with the reliable H∞ control problem against actuator failures for discrete two‐dimensional (2‐D) switched systems with state delays and actuator faults described by the second Fornasini‐Marchesini (FM) state‐space model. By resorting to the average dwell time (ADT) approach, also by constructing an appropriate Lyapunov‐Krasovskii functional and using the Wirtinger inequality, some sufficient conditions for the exponential stability analysis and weighted H∞ performance of the given system are derived. Then, based on the obtained conditions, a reliable H∞ controller design approach is presented such that the resulting closed‐loop system is exponentially stable with a weighted H∞ performance , not only when all actuators are in normal conditions, but also in the case of some actuator failures. Finally, two numerical examples are examined to demonstrate the effectiveness of the proposed results.