Impulsive and switched systems with applications

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There has been a growing world-wide interest in the study of impulsive and switched dynamical systems in recent years. Such systems arise in many applications such as switching circuits in power electronics, orbital transfer and control of spacecrafts, multimedia switching communication networks, drug administration in cancer chemotherapy, interest rate adjustment, constrained impact mechanics, and ecosystems management. However, there are many challenging issues. Firstly, many theorems of continuous dynamical systems fail on impulsive and switched dynamical systems, which is especially so when the systems contain time delay and stochastic disturbance. New ideas need to be developed that deal with impacts, jumps, switching, sliding and chattering problems in a robust and easily applicable way. Secondly, the qualitative understanding of their dynamics requires specific methods and cannot be solved with simple adaptations of known techniques for purely continuous or purely discrete dynamical systems. In this research program, both fundamental research (concepts, criteria and theoretical investigation) and technical development (algorithm design and computer simulation) will be conducted. The proposed research program will result in fundamental theory, comparison methods, invariance principle, stability and robust stability criteria, conditions and algorithms for optimal control, and efficient computational algorithms and software packages for simulation and stabilizing control of impulsive and switched dynamical systems with time delay and stochastic disturbances. Applications to communication networks, secure communication, modeling and control of infectious disease will also be carried out. The outcomes will enhance Canada's reputation for leading edge research and facilitate opportunities for international collaboration. It will also provide an excellent opportunity for research training of highly qualified personnel.