A piecewise ellipsoidal reachable set estimation method for continuous bimodal piecewise affine systems

In this work, the issue of estimation reachable sets in continuous bimodal piecewise affine systems is studied. A new method proposed, framework ellipsoidal bounding, using quadratic Lyapunov functions. Although can be seen as a special class hybrid systems, reachability methods developed for might inappropriately complex dynamics. This work goes direction exploiting dynamical structure system to propose simpler approach. More specifically, because nature function, we first derive conditions ensure that given function positive on half spaces. Then, exploit property functions being hyperplane. Finally, linear matrix characterizations estimate set are derived.