Regolazione dell'uscita ibrida per una classe di sistemi lineari con salti aperiodici

Hybrid systems, which combine continuous and discrete dynamics, offer a highly versatile and powerful framework for understanding, modeling, and controlling complex phenomena in various fields of engineering and science. These systems capture the dual nature of processes that alternate between continuous behaviors and discrete events, such as in walking robots and advanced communication systems. In robotics, hybrid systems are crucial for modeling the movement of walking robots, as they integrate the continuous flow of motion with discrete events that occur when the robot's feet make contact with the ground. This capability to represent smooth transitions and instantaneous events is key to achieving stable, efficient, and adaptable locomotion in dynamic environments. Similarly, in communication systems, hybrid models play an equally important role by enabling the implementation of protocols that require discrete signal changes, while also handling the continuous flow of data. These models are essential for improving the efficiency and robustness of modern communication architectures, which rely on a seamless integration of continuous and discrete dynamics. This dissertation presents an structurally stable solution to the Hybrid Output Regulation problem for a particular class of linear hybrid systems that include exosystems with aperiodic jumps. The proposed approach addresses both the theoretical and practical challenges that arise when controlling systems whose dynamics change abruptly at certain moments, while remaining continuous at others. The first part of this research introduces the problem for a specific class of linear hybrid systems, where controllability and observability are only achieved during aperiodic jumps. In these systems, control interventions are only possible at the jump moments, creating unique challenges in terms of stability and reference tracking. The second part extends the analysis to consider linear hybrid systems that allow control inputs both during the continuous flow phases and at the jump moments. In this context, a switched observer is proposed, which ensures stability through switching signals and a minimum dwell time between jumps. The stability of both control schemes is rigorously analyzed using Lyapunov functions and Linear Matrix Inequality (LMI) techniques, guaranteeing global exponential stability. Finally, simulation results are provided to illustrate the effectiveness of the proposed control schemes and to validate their performance in realistic scenarios.