Worst case identification in discrete and continuous time systems

The problem of system identification is considered for single-input-single-output stable linear discrete- and continuous-time time-invariant systems. Worst-case asymptotic optimal or suboptimal identification methods are sought. The main objective of system identification is to reduce uncertainty of a system via input-output observations. One possibility of modeling uncertainty sets is to use ∈-nets. The concepts of ∈-nets and ∈-dimension are studied and their relationships to system identifiability are exploited. The problem of system identification for discrete-time systems is considered. It is shown that for the algebra of exponentially stable systems, truncation of system kernels leads naturally to a minimal ∈-net. It is demonstrated that finding an asymptotically optimal identification algorithm can be reduced to a minimax problem which can be solved using certain standard mathematical programming algorithms. Properties of the minimax problem are derived. The identification of continuous-time systems via sampling is considered