An algorithm for computationally efficient digital implementation of LTI controllers

In this paper we present an algorithm for computationally efficient digital implementation of linear time invariant controllers. The algorithm transforms a linear time invariant controller into a periodically time varying system, which can be digitally implemented in a computationally efficient manner. This is achieved by first decomposing the controller into a dual rate system. A scheduling policy is adopted that spreads the computation, required to update the states of the slower system, over a time horizon. This reduces the total number of states updated at a given time step and hence the computational overhead. A theoretical framework is also developed to analyse the effect of this transformation on the closed-loop stability performance. The theoretical analysis framework relies on multi-rate filter bank theory and lifting techinique used in the analysis of multi-rate control systems.