This work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed to force the system state onto the predefined switching surface in short time. By using Lyapunov stability theory, some novel results are obtained, and the required stability conditions are established in terms of linear matrix inequalities which can be solved by standard Matlab toolbox. Finally, the results are validated over a Chua’s circuit model, which describes the practical application of the developed results.

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