Feedback linearisation of uncertain nonlinear systems with time delay

On asymptotic stabilisation of a chain of integrators with nonlinearity and an uncertain input delay by output feedback

“…Actually, in this case α(t, x) belongs to (lower) triangular systems whereas many existing results have dealt with feedforward systems (Niculescu and Michiels 2004;Choi and Lim 2006;Mazenc and Bliman 2006;Choi and Lim 2010a;Ye 2011;Zhang et al 2011). Moreover, the results of Choi and Lim (2010b), Roh and Oh (1999) and Shin et al (2006) may be applicable to this system but they are state feedback results. Thus, in this example, we clearly show our advantages over the existing results.…”

“…For nonlinear time-delay systems in feedback linearised forms, there have been several results. In Roh and Oh (1999) and Shin, Choi, and Lim (2006), the reduction-transformation-based controllers are designed for small delay in the input. This small delay restriction is relaxed in Koo, Choi, and Lim (2008) by using a scaled sliding surface, but at the cost of reducing domain of attraction proportional to the delay size.…”

Wheel slip control for ABS with time delay input using feedback linearization and adaptive sliding mode control

“…Using (16), (19), (23), and (23), we check that Lyapunov function V = (1/2)σ T (t)σ(t) + (1/2)γη 2 is negative definite as shown in [1] whereη is the difference betweenη and the upper bound of the uncertainty.…”

“…Now, we design the controller for the anti-lock braking system by referring to the theoretic result [1] in the following. We apply the feedback linearization on the state variable, x, because we would like to make λ track λ d and v remain bounded.…”

“…Note that the remaining term after feedback linearization is regarded as the uncertainties of the system dynamics. Thus, using the linear transformation based on the reduction method shown in [2], we compensate the time delay and design the adaptive sliding mode controller as adapting the bound of the uncertainties [1].…”