Abstract
This chapter aims to study the problem of stability analysis, and robust exponential stabilization for a class of switched linear systems with polytopic uncertainties is reviewed. A sufficient condition based on the average dwell time that guarantees the exponential stability of uncertain switched linear systems is given. First, the iterative learning control is presented to build a formulation ensuring the exponential stability of the given system. The integrated design of this ILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. The results are obtained through original connection with the notion of stability along the pass for 2D repetitive systems. An overview of the stabilization methods of switched discrete systems found in the literature is outlined. All the given formulations are presented in terms of LMIs. A numerical simulation example is established, showing the effectiveness of the proposed method.
Key Terms in this Chapter
Robust Control: A branch of control theory that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modeling errors.
Polytopic Uncertainties: Parametric uncertainties. The matrix of the state system is a linear combination of convex and belongs to the field type polytopic.
Linear Matrix Inequality and Control Theory: The LMI that arise in system and control theory can be formulated as convex optimization problems, and hence are amenable to computer solution.
Iterative Learning Control (ILC): A method of tracking control for systems that work in a repetitive mode. Examples of systems that operate in a repetitive manner include robot arm manipulators, chemical batch processes and reliability testing rigs. In each of these tasks the system is required to perform the same action over and over again with high precision. This action is represented by the objective of accurately tracking a chosen reference signal on a finite time interval.
Hybrid System: A dynamic system that exhibits both continuous and discrete dynamic behavior a system that can both flow (described by a differential equation) and jump (described by a difference equation or control graph). Often, the term “hybrid dynamic system” is used, to distinguish over hybrid systems such as those that combine neural nets and fuzzy logic, or electrical and mechanical drivelines. A hybrid system has the benefit of encompassing a larger class of systems within its structure, allowing for more flexibility in modelling dynamic phenomena.
Dwell Time Switching: Logic for orchestrating the switching between controllers in a family of candidate controllers in order to control a process with a highly uncertain model.
Switched system: A hybrid dynamical system defined by a family of subsystems and a switching rule orchestrating the switching between subsystems.