Polynomial operator-based digital controller structures of high stability performance and computation efficiency

Non-fragile H∞ filter design with sparse structure for linear discrete-time systems

“…(22). As an extension of the fact, we have the following result for system (12) with the filter gain variations. holds for all ΔA F , ΔB F and ΔC F satisfying Eq.…”

“…When the filter parameter matrices A F ; B F and C F are known, the following lemma presents a sufficient condition for evaluating the non-fragile H 1 performance of system (12). Denote …”

“…It is well known that the computational efficiency is critical in real time applications, so it is highly desirable for a controller to have a sparse structure, namely containing many trivial parameters (trivial parameters mean that they are 0 and 71, which can be digitally implemented exactly and cause no rounding errors; other parameters are, therefore, referred to as nontrivial parameters [7]). The problem of finding sparse controller realizations has been considered by several researchers, such as [1,7,12,13,15,16,19,27] where two classes of sparse controller structures characterized with a set of free parameters are derived in [12], and a stepwise algorithm is applied to make the controller realization sparse in [16]. In [7], based on a polynomial operator approach, a new sparse controller realization is derived.…”