UC Santa Cruz

This dissertation focuses on a class of observer designs for linear-time invariant (LTI) systems, where the state variables are typically not directly measurable or may be too expensive to completely measure. Designing an observer with both fast convergence rate and robustness to noise is a well-know challenge, yet it is an essential task in many applications. To relax the generic tradeoff between fast convergence rate and robustness to perturbations in observer design with static gains, three main scenarios are considered in this thesis. With the assumption that information is accessible continuously (discretely), the first case focuses on interconnected observers over a network. It is shown to have significant advantages when comparing to a Luenberger observer. The second scenario is when the rate of convergence is prioritized. A robust observer that exhibits both continuous and impulsive behaviors is developed. With proper choice of parameters, such an observer generates estimates that converge to the state of LTI in finite-time and is robust to small perturbations. The third scenario is when measurements and information over networks are only accessible intermittently. A hybrid distributed state observer framework is established to achieve global exponential stability of the zero estimation error set. Its robustness with respect to measurement, communication noise and unmodeled dynamics is characterized in terms of input-to-state stability (ISS). In addition to providing sufficient conditions to guarantee stability and robustness of these observers, the problem of determining parameters are characterized by Linear Matrix Inequalities (LMIs) in this thesis. Constructive LMIs based on Lyapunov methods are given to efficiently design these observers. Advantages and unique properties of these observers are illustrated in many examples throughout the thesis.