Variable Structure Control of Second Order Systems With Nonlinear Uncertain Discontinuous Input Functions Using Approximate Inverses

We consider second order nonlinear systems in control canonical form, where the functional relation between variable and system acceleration is nonlinear, uncertain discontinuous. approximate discontinuous function with an invertible one, use structure theory to suppress error of inverse. rewrite finite time reaching law or terminal into form inequalities these design a that drives state sliding surface time, one ensures convergence speed position errors narrow, adjustable width band around zero. The stability also analyzed proven. demonstrate how ensure sufficiency available effort, by proper parameters. method then validated on numerical model input function.