Discussion on: “Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty”

Abstract

ðm p < nÞtheoutput; gðx,tÞisthematcheduncertainty and fðx,tÞ the unmatched uncertainty; ðxÞ is a known nonlinear vector function with ð0Þ¼0.The authors use the ideas of robust sliding modecontrol and incorporate a sliding surface originallyproposed by Edwards and Spurgeon [2]. The dis-continuous sliding mode control has been describedfully elsewhere (see, e.g. [4,7,9]). Using the estimatedstates and the system output, a dynamic slidingmode control is developed which is shown to satisfythe well-known reachability condition [7,9]. A non-linear asymptotic observer is proposed and this yieldsexponential state estimation error convergence basedon the solution to a constrained Lyapunov equation.Both matched and unmatched system uncertaintiesare considered. Like all sliding mode control systems,the following important property holds: the systembehaviour is invariant to the matched uncertaintyduring the sliding mode [9].The authors impose two realistic assumptions thatguarantee the existence of the output sliding mode[1,2]. Also assumed are the assumptions that the pair(A, C) is observable and that the nonlinear function ðxÞ is Lipschitz and that there exist known con-tinuous functions