Abstract
This chapter is concerned with the problem of robust non-fragile ℌ2 controller design for linear time-invariant discrete time systems with uncertainty. The controller to be designed is assumed to have additive gain variations or multiplicative gain variations, which are due to the finite word-length (FWL) effects when the controller is implemented. Sufficient conditions for the robust non-fragile control problem are given in terms of solutions to a set of matrix inequalities. The resulting design is such that the closed-loop system is robustly stable and has an ℌ2 cost bound against plant uncertainty and controller gain variations. Iterative linear matrix inequalities (LMI) based algorithms are developed. Numerical examples are given to illustrate the design methods.
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