Discontinuous dynamical systems and multiagent systems are encountered in numerous engineering applications. This dissertation develops stability and dissipativity of nonlinear dynamical systems with discontinuous right-hand sides, optimality of discontinuous feed-back controllers for Filippov dynamical systems, almost consensus protocols for multiagent systems with innaccurate sensor measurements, and adaptive estimation algorithms using multiagent network identifiers. In particular, we present stability results for discontinuous dynamical systems using nonsmooth Lyapunov theory. Then, we develop a constructive feedback control law for discontinuous dynamical systems based on the existence of a nonsmooth control Lyapunov function de fined in the sense of generalized Clarke gradients and set-valued Lie derivatives. Furthermore, we develop dissipativity notions and extended Kalman-Yakubovich-Popov conditions and apply these results to develop feedback interconnection stability results for discontinuous systems. In addition, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Then, we provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Furthermore, we address the consensus problem for a group of agent robots with uncertain interagent measurement data, and show that the agents reach an almost consensus state and converge to a set centered at the centroid of agents initial locations. Finally, we develop an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies that identifies the system state and plant parameters online.

Power electronics applications in high power are normally large, expensive, spatially distributed systems. These systems are typically complex and have multiple functions. Due to these properties, the control algorithm and its implementation are challenging, and a different approach is needed to avoid customized solutions to every application while still having reliable sensor measurements and converter communication and control. This thesis proposes a synchronous digital control architecture that allows for the communication and control of devices via a fiber optic communication ring using digital technology. The proposed control architecture is a multidisciplinary approach consisting of concepts from several areas of electrical engineering. A review of the state of the art is presented in Chapter 2 in the areas of power electronics, fieldbus control networks, and digital design. A universal controller is proposed as a solution to the hardware independent control of these converters. Chapter 3 discusses how the controller was specified, designed, implemented, and tested. The power level specific hardware is implemented in modules referred to as hardware managers. A design for a hardware manager was previously implemented and tested. Based on these results and experiences, an improved hardware manager is specified in Chapter 4. A fault tolerant communication protocol is specified in Chapter 5. This protocol is an improvement on a previous version of the protocol, adding benefits of improved synchronization, multimaster support, fault tolerant structure with support for hot-swapping, live insertion and removals, a variable ring structure, and a new network based clock concept for greater flexibility and control. Chapter 6 provides a system demonstration, verifying the components work in configurations involving combinations of controllers and hardware managers to form applications. Chapter 7 is the conclusion. VHDL code is included for the controller, the hardware manager, and the protocol. Schematics and manufacturing specifications are included for the controller. / Master of Science