Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 826438 19 pages doi 2009 826438 Research Article Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems M. De la Sen Department of Electricity and Electronics Institute of Research and Development of Processes Faculty of Science and Technology University of the Basque Country Campus de Leioa Bizkaia 644 Apertando de Bilbao 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 26 March 2009 Accepted 20 May 2009 Recommended by Juan J. Nieto Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems by using the powerful tool of fixed point theory. The class of hybrid systems dealt consists in general of coupled continuous-time and digital systems subject to state perturbations whose nominal . unperturbed parts are linear and in general time-varying. The obtained sufficient conditions on robust stability under a wide class of harmless perturbations are dependent on the values of the parameters defining the overbounding functions of those perturbations. The weakness of the coupling dynamics in terms of norm among the analog and digital substates of the whole dynamic system guarantees the total stability provided that the corresponding uncoupled nominal subsystems are both exponentially stable. Fixed point stability theory is used for the proofs of stability. A generalization of that result is given for the case that sampling is not uniform. The boundedness of the state-trajectory solution at sampling instants guarantees the global boundedness of the solutions for all time. The existence of a fixed point for the sampled state-trajectory solution at sampling instants guarantees the existence of a fixed point of an extended auxiliary discrete system and the existence of a global asymptotic .
