Reliable control of discrete-time systems via LEQG performance criteria

In this study, results obtained by Veillette (1995) for continuous systems are extended to the study of linear-exponential-quadratic-Gaussian (LEQG) type reliable control for discrete-time systems which can tolerate abnormal operation within some pre-specified set of actuators. This is achieved by suitable modification of the algebraic Riccati equation (ARE) for the design of the controller. Using the LEQG controller´s Kalman gain, we show that the stability of the overall system is preserved despite the abnormal operation of actuators within a pre-specified subset. The gain margin of the feedback gain for reliable stabilization is also derived, which is shown to agree with the one obtained by Veillette for the continuous case when the sampling time is sufficiently small.