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This study proposes a class of variable structure stabilizing laws which make the closed-loop system be capable of tolerating the abnormal operation of actuators within a pre-specified subset of actuators. The ranges of acceptable change in control gain magnitude that preserves system's stability are estimated for the whole set of actuators. These ranges are shown to be able to be made larger than those obtained by linear quadratic regulator (LQR) reliable design (Veillette, 1995, and Liang, 2000) by the choice of control parameters. Besides, this approach does not need the solution of Hamilton-Jacobi (HJ) equation or inequality, which is essential for optimal approaches such as LQR and H infin reliable designs. As a matter of fact, this approach can also relax the computational burden for solving the HJ equation or inequality
Liang et al. (Sun,) studied this question.