Finite-horizon, discrete-time variable tolerance H∞ filtering

The discrete-time, variable tolerance H-infinity filtering problem is presented. The variable tolerance is specified at every time sample and guarantees a feasible tolerance value without an iterative design process. The variable tolerance H-infinity filtering problem generalizes the standard constant tolerance H-infinity filtering problem and, as a result, leads to a straightforward procedure for approximating the optimal value, gamma inf, of the constant tolerance problem. Furthermore, the more general setting of the variable tolerance problem admits an improved H-infinity filter with a smaller L2 gain than the constant tolerance H-infinity filter. Applications of a variable tolerance to the H-infinity control problem are discussed as well.