Compactly supported wavelets have certain properties that are useful for controller design. We explore the mechanism of a wavelet controller by integrating the wavelet controller with linear time-invariant systems (LTI). A necessary condition for an effective wavelet-based control is that the footprints of the wavelet network cover the state space where the state trajectories stay. Closed-form bounds on the design parameters of a wavelet controller are derived, which guarantee local asymptotic stability of wavelet-controlled LTI systems. Wavelet network is also effective in adaptive control of chaotic systems when there are uncertainties with the system. In this case, global stability of wavelet-control Lorenz system along with classical state feedback control is investigated.