Stabilization of hybrid systems using a min-projection strategy

This paper describes a method of how to stabilize a system consisting of several subsystems. The subsystems are described by nonlinear models with different vector fields. The method is denoted the min-projection strategy, since the vector field associated with the smallest (skew) projection is selected for each state. Conditions are given guaranteeing (exponential) stability. It is also shown how these conditions can be formulated as a nonlinear optimization problem, or, for a pre-determined projection matrix, a linear matrix inequality (LMI) problem. Sliding motions may occur in the basic form of the strategy. However, it is shown how this behavior can be avoided by introducing hysteresis around the switch surfaces, still preserving the stability of the closed-loop hybrid system. Two examples are given to motivate and exemplify the strategy.