An impulsive framework for the control of hybrid systems

An impulsive control formulation suitable for analyzing hybrid systems is presented. Besides a continuous evolution, the trajectory of an impulsive control system may also exhibit jumps. The jump trajectory is well characterized in this impulsive framework. These jumps can be interpreted as the discrete evolution of an hybrid system. Several examples of hybrid systems modeled in the impulsive framework are given. An impulsive formulation of a formation control problem, regarded as an hybrid system is detailed. Finally, an overview of important classes of control results available for impulsive control systems, notably, stability and optimality, attest the importance of this paradigm for the control of hybrid systems. These results are essential to investigate the properties of model predictive control schemes for hybrid systems.