Switched linear systems are noted as a major category of control systems‎. ‎Fault detection of these systems is affected by switching phenomena and therefore their integrated fault detection and robust control (IFDRC) are the central issues of recent studies‎. ‎Existing studies on IFDRC do not consider the effects of all of the parameter uncertainties‎, ‎input disturbance‎, ‎and mode-dependent time-varying state delay in the presence of mode-dependent average dwell time (MDADT) switching together in these systems. To address the issue based on output feedback‎, ‎in this paper‎, ‎the IFDRC design problem is formulated as a multi-objective or mixed H∞/H- optimization problem‎. ‎H∞ performance indicator guarantees the robustness of residual to disturbance‎, ‎and H- performance represents the sensitivity index of residual to the fault‎. ‎A piecewise Lyapunov-Krasovskii function is employed together with the MDADT scheme and therefore‎, ‎sufficient conditions are derived in terms of linear matrix inequalities (LMIs) in order to deal with the problem‎. ‎Then to clarify the design procedure‎, ‎we also present an algorithm in the light of the proposed approach‎. ‎Eventually‎, ‎to illustrate the efficiency of the suggested approach‎, ‎the designed IFDRC framework is simulated for a case study of an Electrical Circuit system.