Analysis and Synthesis of Nonuniformly Sampled Systems

Sampled-data control theory is the mathematical foundation required for the analysis and design of sampled-data systems. An important assumption in the development of conventional sampled-data control theory is that measurement sampling periods are uniform. However, with the widespread use of networked and embedded control systems it is not possible or practically feasible to have constant measurement sampling periods. Consequently, the conventional sampled-data theory needs to be re-evaluated before designing this class of control systems. Motivated by this, this thesis develops mathematical approaches for the analysis and synthesis of sampled-data systems with nonuniform sampling periods.;Two types of variations in sampling period are considered. For the first type, we assume that the measurement is sampled irregularly but the input is updated regularly. For the second type, we assume that both measurement sampling and input updating occur synchronously but with nonuniform intervals. These timing models are general enough to capture many different types of variations in sampling periods.;Both state estimation and control problems are considered. For state estimation, two types of filters are developed: a sampling period dependent for the first type of variations and a robust one for the second type of variations. A novel Markov model of the irregular sampling process together with the theory of Markovian jump systems lead to the design of the first type of filter. The second filter is designed by modelling the nonuniform sampling system as uncertain feedback system with linear fractional transformation uncertainty. For the control problem, a dynamic robustly stabilizing output feedback controller and a robust H∞ controller are developed. Both controllers are designed for the second type of variations in sampling period and analysis is based on modelling the nonuniform sampling system as uncertain feedback system.;All theoretical development in this thesis is in discrete time and design conditions are formulated as linear matrix inequalities (LMI's). Many solvers, such as the LMI toolbox of MATLAB, exist and can solve these convex optimization problems very efficiently. Most constant-parameter filters or controllers designed are easily implemented. The effectiveness of the proposed filters or controllers is demonstrated using simulation results.