Fast finite-time partial state feedback stabilization of high-order nonlinear systems with output constraint and dynamic uncertainties

Disturbance attenuation with fast global finite‐time convergence for generalized high‐order uncertain nonlinear systems

“…Specifically, Figures 1 and 2 show the influence on the convergence of the state variables for different and m 1 . Figures 3 and 4 illustrate that the convergent time of fast finite-time stabilizer in this paper is obviously superior to the traditional finite-time ones [20][21][22][27][28][29]31 for m 1 = 1, = 1. Figures 5 and 6 show the influence on the convergence for = 0 or = 10 (1+t 2 ) 3∕4 and m 1 = 1, = 1.…”

“…the proof of (29) can be find in the work of Sun et al, 42 and the proof of (30), (31) is placed in the Appendix. By (29)-(31), applying Lemmas 1-3, (1), and (22), we get…”

“…(i) This paper is the first work on the problem of disturbance attenuation for high‐order uncertain nonlinear systems (eg, system ) with global fast FTC. Moreover, the convergent time of fast finite‐time stabilizer is obviously superior to the existing ones . (ii) A new perspective on achieving both disturbance attenuation and fast FTC issues is presented, thereby providing a solution to fill the gap of lacking disturbance attenuation control with fast FTC.…”

“…What is important is that sliding mode control strategy was introduced in other works [23][24][25] to solve finite-time control in the presence of uncertain parameters and disturbances. Readers can also consult other elegant studies [26][27][28][29][30][31][32][33][34][35][36][37][38] Compared with the asymptotic one, the FTC usually exhibits some distinct features which are important for demanding applications, such as fast response, higher control accuracy, and better robustness to uncertainties. However, as pointed out in the work of Moulay and Perruquetti, 39 it is in general not easy to construct a suitable/desired Lyapunov function to claim FTC, especially in a complex environment; besides, the system with FTC usually possesses in nature a slower convergence rate than the exponential one especially when the initial state is far away from the origin.…”

“…Moreover, the convergent time of fast finite-time stabilizer is obviously superior to the existing ones. 20,22,[27][28][29]31 (ii) A new perspective on achieving both disturbance attenuation and fast FTC issues is presented, thereby providing a solution to fill the gap of lacking disturbance attenuation control with fast FTC. In addition, the convergent time can be adjusted by choosing different design parameters, which improves the potential drawbacks in finite-time control.…”