Abstract

A dynamical system's state evolves over time, and when the system stays near a particular state this state is known as a stable state of the system. Through control methods, dynamical systems can be manipulated such that virtually any state can be made stable. Although most real systems evolve continuously in time the application of digital control methods to these systems is inherently discrete. States are sampled (with sensors) and fed back into the system in discrete-time to determine the input needed to control the continuous system. Additionally, dynamical systems often experience time delays. Some examples of time delays are delays due to transmission distances, processing software, sampling information, and many more. Such delays are often a cause of poor performance and, at times, instability in these systems. Recently a criterion referred to as intrinsic stability has been developed that ensures that a dynamic system cannot be destabilized by delays. The goal of this thesis is to broaden the definition of intrinsic stability to closed-loop systems, which are systems in which the control depends on the state of the system, and to determine control parameters that optimize this resilience to time delays. Here, we give criteria describing when a closed-loop system is intrinsically stable. This allows us to give examples in which systems controlled using Linear Quadratic Regulator (LQR) control can be made intrinsically stable.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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