An iterative LMI method to discrete-time reliable state-feedback controller design with mixed H₂H_∞ performance

This paper studies the reliable mixed H₂/H_∞ state-feedback control of discrete-time linear systems based on the iterative linear matrix inequality (ILMI) approach. The design goal is to find an internally stabilising state-feedback controller such that the nominal mixed H₂/H_∞ performance measure of a closed-loop transfer matrix is optimized. The designed controller satisfies the H_∞ robust stability constraint and the reliability constraint (in terms of stability and performance) under actuator faults. Besides the advantage of optimizing nominal performance, this new reliable design has the flexibility that it can be formulated to tolerate the actuator faults within certain admissible set of actuators, or to tolerate any single actuator fault. Either partial or complete actuator fault is allowed. Two examples are also given to illustrate the design method and benefits.