Our following papers were accepted for publication in Automatica and IEEE Transactions on Automatic Control, I have updated the preprint and will add bibliographical data as soon as possible.
Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco
In: IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1513-1528, 2021.
Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. In the first part of the paper the feasible Filippov solution concept is introduced by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. Several examples illustrate the theoretical arguments and the effectiveness of the stability result.
Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan
In: Automatica, vol. 119, no. 109100, 2020.
The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability conditions in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability.
[Update] For the Automatica paper there is a 50-day free download available.