Sampled-Data Filtering and Control of Linear Parameter Varying Systems with Delay

In this dissertation we address a variety of problems in filtering and control of dynamic systems with emphasis on their digital implementation. We focus on linear parameter varying (LPV) systems which have been widely utilized in engineering applications. LPV systems include a class of linear systems whose dynamic depends on time-varying parameters. These systems have resulted in significant improvements in the study of time-varying and nonlinear systems.

In a filtering problem, we aim to estimate the states of a dynamic system by utilizing the output measurement of the system. Applications of filters abound in practical and theoretical problems. In a control problem, the objective is to design a controller to ensure the closed-loop system stability and often to satisfy a prescribed level of performance. A main concern in the present study is the implementation of the controller or filter which is often fulfilled by means of a digital device operating in the discrete time domain. Due to the combination of the system continuous-time dynamics and the controller or filter discrete dynamics connected through analog to digital and digital to analog converter devices, the closed-loop system is a hybrid one and is difficult to analyze mathematically. The incorporation of continuous-time and discrete-time signals in a system is often referred to as sampled-data system. A particular difficulty in sampled-data systems is to ensure that the digital controller (filter) meets the design specifications in between the samples. In this dissertation, we develop new methods to take into account this requirement.

Two chapters of this dissertation are devoted to the design of filters for LPV systems. First, we design a continuous-time filter for a continuous-time state-delayed LPV system whose dynamics includes a time varying delay. Next, we address the sampled-data filter design problem for continuous-time LPV systems. In the second part of this dissertation, we investigate the control problem of LPV systems in the framework of sampled-data design. First we present a new approach for the sampled-data control of continuous-time LPV systems. Next, we extend the established results for LPV systems with internal delay.