The radio frequency (rf) self-bias of the substrate in a rf inductively coupled plasma is controlled by means of varying the impedance of an external LC network inserted between the substrate and the ground. Experimental studies were done on the relations of the tuned substrate self-bias with varying discharge and external circuit parameters. Under a certain discharge gas pressure, the curves of tuned substrate self-bias Vtsb versus tuning capacitance Ct demonstrate jumps and hysteresises when rf discharge power is higher than a threshold. The hysteresis loop in terms of ACtcrit1 (= Ccrit1 - Ccrit2, here, Ccrit1, Ccrit2 are critical capacitance magnitudes under which the tuned substrate self-bias jumps) decreases with increasing rf discharge power, while the maximum | Vtsbimn | is achieved in the middle discharge-power region. Under a constant discharge power |Vtsb min|, Ctcrit1 and Ctcrit2 achieve their minimums in the middle gas-pressure region.When the tuning capacitance is pre-set at a lower value, Vtsb varies slightly with gas-flow rate;in the case of tuning capacitance sufficiently approaching CtcritX, Vtdb undergoes the jump and hysteresis with the changing gas-flow rate. By inserting a resistor R into the external network,the characteristics of Vtsb - Ct curves are changed with the reduced quality factor Q depending on resistance values. Based on inductive- and capacitive-coupling characteristics of inductively coupled plasma, the dependence of a plasma sheath on plasma parameters, and the impedance properties of the substrate branch, the observed results can be qualitatively interpreted.