Risk-sensitive filter for linear discrete-time systems with multiple time-delay measurements

The risk-sensitive filtering problem is considered for linear discrete-time systems with time-delay measurement processes which are described by l + 1 channels. The problem can be converted into an optimization problem with quadratic form. By introducing an auxiliary state-space model, we can use indefinite space approach to solve the optimization problem and design risk-sensitive filter with the help of the innovation analysis. Furthermore, the necessary and sufficient conditions of existence for the risk-sensitive filter will be given when the risk-sensitive parameter is negative. (The risk-sensitive filter always exists when the risk-sensitive parameter is positive.)