**2. Spatial‐based output feedback linearization robust adaptive repetitive control (OFLRARC)**

Consider the state‐variable model of an *n*th‐order single‐input single‐output NTI system with model uncertainties and output disturbance, i.e.,

$$\begin{aligned} \dot{\mathbf{x}}(t) &= \left[ f\_t \left( \mathbf{x}(t), \boldsymbol{\phi}\_f \right) + \Delta f\_t \left( \mathbf{x}(t), \boldsymbol{\phi}\_f \right) \right] + \left[ \mathbf{g}\_t \left( \mathbf{x}(t), \boldsymbol{\phi}\_s \right) + \Delta \mathbf{g}\_t \left( \mathbf{x}(t), \boldsymbol{\phi}\_s \right) \right] \mathbf{u}(t) \\ \mathbf{y} &= \Psi \mathbf{x}(t) + d\_y \left( t \right) = \mathbf{x}\_1(t) + d\_y(t) \end{aligned} \tag{1}$$

where *x*(*t*)= *x*<sup>1</sup> (*t*) ⋯ *xn*(*t*) *<sup>T</sup>* , *Ψ* = 1 0 ⋯ 0 , *u*(*t*), and *y*(*t*) correspond to the control input and measured output angular velocity of the system, respectively.
