Parametric Optimization of Non-Integer Order PD $$^\mu $$ μ Controller for Delayed System

Convergence of Laguerre Impulse Response Approximation for Noninteger Order Systems

“…In this paper, we have shown theoretical basis and actual effectiveness of LIRA method for approximating noninteger order systems. As it can be seen (documented in earlier works, i.e., [21][22][23][24]35]), it is an approximation of inputoutput relationships, adequate for such purposes like filtering or control loop optimization. The main contribution of this paper over the earlier results was relaxation of the assumptions regarding the impulse response of approximated system, as it is no longer required for it to be bounded.…”

“…In [20], it was shown that under certain assumptions method is convergent in L 1 and L 2 norms when approximating asymptotically stable noninteger transfer functions of relative degree equal to or greater than one. Most applications of the method can be found in filtering and parametric optimization [21][22][23]. In [24], it was shown that in certain cases and at low orders of approximation LIRA outperforms Oustaloup method.…”

On Digital Realizations of Non-integer Order Filters

“…It introduces substantial improvements such as L 1 convergence, estimation of approx-imation error and choice of optimal approximation basis. For examples of use, see [46][47][48].…”