Comments on "On the stability of discrete-time sliding mode control systems" [with reply]

In the above paper by S.Z. Sarpturk and Y. Istefanopulos (see IEEE Trans. Automat. Contr., vol.AC-32, p.930-2 (1987)), stability conditions for discrete-time sliding mode control systems are presented, which require the stabilizing control to be upper and lower bounded. The present author shows that these bounds depend on the distance of the system state from the sliding manifold and that they converge as the state approaches the manifold. Sarpturk and Istefanopulos agree that the bounds of the discrete-time control guaranteeing the stability of the sliding mode system depend also on the distance of the state from the sliding manifold. Therefore, in order to guarantee the stability of the sliding mode system, the controls must be chosen so as to satisfy the convergence and sliding bounds derived in the paper.>