A Lyapunov based Method for Designing State Feedback Controllers for a class of Discrete-time Systems

Abstract

In this work, we look at a family of problems that restrict the input moves allowed. Optimal solutions of these problems turn out to be solutions of other problems. From these relations, we develop a novel interpretation for controller design in terms of a search for a Lyapunov function with a prescribed rate of decay dependent on states and inputs. We demonstrate how this method connects with LQOC. The efficacy of the proposed controller design approach is demonstrated using the benchmark quadruple tank system operated at the non-minimum phase operating point. Analysis of the simulation results reveal that, the controller tuning matrices can be effectively used for shaping state error and manipulated input profiles similar to the quadratic optimal control formulation.