Output feedback finite‐time dissipative control for uncertain nonlinear fractional‐order systems

Abstract

This paper solves the robustly finite‐time dissipativity control problems for uncertain nonlinear fractional‐order systems (FOS). Firstly, by using some basic mathematical transformations associated with linear matrix inequality (LMI) techniques, a novel condition for the existence of output feedback controllers is established to ensure the closed‐loop FOS is finite‐time stabilizable. Then, based on the proposed stabilization criterion combined with some well‐known properties of fractional calculus, the finite‐time dissipativity control problem for nonlinear FOS subject to uncertainties is studied for the first time. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

An improved output feedback controller design for linear discrete‐time systems using a matrix decomposition method

“…Finally, pre-multiplying and post-multiplying by diag{I, G} and diag{I, G T }, respectively, and thereby replacing −GP −1 G T with the bounding inequality, −GP −1 G T ≤ −Sym{G} + P [35], one obtains (5). Using similar steps, it can be shown that ( 6) is sufficient for (9). The proof is complete.…”

“…However, this design method becomes tedious with increasing number of state variables, since it involves the dynamics of both the system as well as the observer. Thus, to alleviate this problem, output feedback is generally preferred in many practical applications, for instance, in the works [5][6][7][8][9][10]. With output feedback, only the information of the measurable output is required.…”

Finite‐time dissipative control for semi‐Markovian jump systems with time‐varying delays and generally uncertain transition rates

“…Nowadays, people are more interested in the transient performance of systems in a finite time, that is, in a limited time interval [21][22][23][24][25][26][27][28][29][30]. Finite-time stability is introduced to deal with these transient performances.…”

Stabilization for nonlinear fractional‐order time‐varying switched systems

“…Note that nonlinearity is universal for practical systems. Naturally, fractional-order nonlinear dynamic systems have gained considerable attentions [4][5][6][7][8][9][10]. To name a few, together with neuro-fuzzy network approach, an adaptive output feedback control scheme was proposed in Song et al [7] to handle the tracking problem for the fractional-order systems with unknown nonlinearities.…”