No abstract

Switched systems in which switching among subsystems occurs at random time instants find numerous applications in engineering. Stability analysis of such systems, however, is quite challenging. This paper investigates the stochastic inputto-state stability of this class of switched systems. The random switching instants are modeled by a non-decreasing, positive, and real-valued Lévy process, which, at every time instant, selects the active subsystem from a family of deterministic systems. No assumption on the stability of subsystems is presumed; they can be stable or unstable. Stochastic properties of the switching signal are coupled with a family of Lyapunovlike functions to obtain a sufficient condition for stochastic input-to-state stability.

These lecture notes provide an overview of recent research on the modeling and control of smart grids using distributed algorithms. In particular, energy-based modeling of general AC power networks using the framework of port-Hamiltonian systems theory is presented, and the relevance of such a formulation for stability analysis and control design is discussed. Low-level control design aspects (at a physical layer) for DC microgrids are also considered, achieving objectives such as fair load sharing among distributed generation units and (average) voltage regulation using limited data and measurements from the system. Finally, general frameworks for the optimal control of smart grids are introduced to consider both physical and economic constraints and exploit the flexibility brought up by storage devices and demand response from the grid’s prosumers.