Analysis and design of multiscale controllers for linear systems

Multiscale theory has been used in the signal processing area and modeling of some physical and chemical processes since the early 1990s. This theory provides systematic methods to project a signal onto orthogonal subspaces, each containing signal information at a different resolution, which could be useful for the design of control systems. However, there has not been much work done to determine the capabilities and properties of controllers obtained using multiscale theory. In this paper we describe a method to construct and we show some of the properties of linear multiscale controllers for linear time-invariant systems using finite-duration discrete wavelet functions.