Discrete-time H^∞ filtering with initial condition

Abstract

We consider the problem of finite horizon discrete time H^∞ filtering with uncertain initial condition. An H^∞ norm-like performance measure that explicitly accounts for the effect of the initial condition is proposed. Conditions are then derived for the existence and construction of a strictly causal sub-optimal estimator that achieves a pre-specified value of this performance measure. It is also shown that the achievable infimum value of this measure would in general depend on the structure and magnitude of uncertainty present in the initial condition of the system.

Keywords:

• H∞ estimation
• Discrete-time filtering
• Time-varying systems
• Initial condition