Ensuring cybersecurity in networked control systems is a big challenge, especially when wireless channels are used for transmissions of measurement and control data. These channels are subject to a variety of critical threats, among which jamming attacks appear to be one of the easiest to achieve from the perspective of an attacker. Here we look at the problem of controlling a discrete-time linear system over an insecure wireless channel that faces jamming attacks. We consider a channel model based on Signal-to-Interference-plus-Noise Ratio (SINR), where the likelihood of transmission failures at each time can differ depending on the power of the interference signal emitted by a jamming attacker at that time. We investigate state-dependent jamming attacks, where the attacker uses the information of the system state and the dynamics to efficiently change the interference power to cause instability. We analyze the stability of the networked control system by investigating the properties of a martingale that depends on the transmission failure indicator and the interference power process. We then obtain sufficient stability conditions indicating that closed-loop stability can be guaranteed if the attacker has energy constraints and the average jamming interference power has a sufficiently small upper bound. The effect of state-dependent jamming and the utility of our analysis approach is illustrated through an attack strategy with rolling-horizon optimization, where the attacker decides the interference power based on maximizing a utility function that involves the predicted future states given the present state information.