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A maximum-phase system is the opposite of a minimum phase system. A causal and stable LTI system is a maximum-phase system if its inverse is causal and unstable. That is, 1  The zeros of the discrete-time system are outside the unit circle.
The phase oscillator. A phase oscillator is an oscillator model where we view the state of the system as going around the simplest loop, a unit circle. In a phase oscillator model, the state variable $\theta$ is called the phase of the oscillator. The state space in which the phase $\theta$ lives is the interval $[0, 2\pi]$.