Normally, Lyapunov based adaptive control design guarantees the global
boundedness of estimated paramter and all the closed-loop states. But
in the system parameter estimation--the parameter adaptation/update
law, e.g.,

\dot \theta(t)=-sgn(kp)\gamma_1e(t)y(t)

there is always a tuning coefficient, i.e., \gamma, which theoritically has nothing to do with stability. However, actually, if this tuning coefficient is chosen to be too large, the closed-loop system will blow up.

Any body knows why? Somebody tells me that discrepancy between theory and simulation is perhaps that the theory is for a true continuous time system while the simulation only approximates a continuous time system. But even for discrete-time system, the same problem exist, so I am confused....

\dot \theta(t)=-sgn(kp)\gamma_1e(t)y(t)

there is always a tuning coefficient, i.e., \gamma, which theoritically has nothing to do with stability. However, actually, if this tuning coefficient is chosen to be too large, the closed-loop system will blow up.

Any body knows why? Somebody tells me that discrepancy between theory and simulation is perhaps that the theory is for a true continuous time system while the simulation only approximates a continuous time system. But even for discrete-time system, the same problem exist, so I am confused....