Analysis and Design of Aperiodic Sampling Strategies for Nonlinear Control Systems

In the design of modern control systems such as networked control systems and real-time systems with shared computational resources, effects caused by sampling cannot be neglected. Admitting aperiodic sampling patterns bears the potential to greatly improve the resource efficiency for such systems. To account for this, we develop in this thesis techniques for the analysis and design of aperiodic sampling strategies. First, we present an approach for the stability analysis of aperiodic sampling patterns with average constraints on the sampling intervals based on hybrid systems techniques. Second, we present an event-triggered control framework, i.e., a framework for the online design of sampling patterns based on a continuously evaluated triggering rule event-triggered control. The framework is based on signal norms and allows to embed a large class of triggering rules. It serves as a basis for the development of novel triggering rules and yields guarantees for Lp stability are obtained. Third, we present a framework for dynamic self-triggered control. Instead of evaluating a triggering rule continuously, for STC, the next sampling instant is determined at each sampling instant using information available at this time. The proposed framework is based on hybrid system techniques and a dynamic variable that encodes the past system behavior. Guarantees for input-to-state stability or respectively stability of an invariant set are derived for the resulting STC mechanisms.