Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems

In this paper, we formulate the problem of characterizing the stability of a piecewise affine (PWA) system as a verification problem. The basic idea is to take the whole Rn as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semi-global stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as "asymptotically stable in T steps" the trajectories that enter an invariant set around the origin within a finite time T, or as "unstable in T steps" the trajectories which enter a (very large) set Xinst. Subsets of X(0) leading to none of the two previous cases are labeled as "not classifiable in T steps". The domain of asymptotical stability in T steps is a subset of the domain of attraction of an equilibrium point, and has the practical meaning of collecting initial conditions from which the settling time of the system is smaller than T. In additio...

• Type: Conference
• Year: 2000
• Where: HYBRID
• Authors: Alberto Bemporad, Fabio Danilo Torrisi, Manfred Morari
• Keywords: Control Systems, Finite Time, HYBRID 2000, Initial Conditions, Trajectories