Finite-Horizon, Discrete-Time Variable Tolerance H Filtering

The discrete-time, variable tolerance H_infin 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_infin filtering problem generalizes the standard constant tolerance H_infin 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_infin filter with a smaller L₂ gain than the constant tolerance H_infin filter. Applications of a variable tolerance to the H_infin control problem are discussed as well.