Kanat Camlibel

Complementarity and passivity for piecewise linear feedback systems

Piecewise linear feedback systems composed by a dynamical linear time invariant system closed in feedback through a static piecewise linear mapping are considered. By representing the closed loop system in the affine complementarity form, passivity is exploited in order to prove existence of absolute continuous solutions and stability of the equilibria. Assuming passivity of the open loop system and using results on equivalent circuit representations of piecewise linear mappings, conditions on the static feedback connection for preserving passivity in closed loop, are proposed and discussed

Stabilizability of bimodal piecewise linear systems with continuous vector field

This paper studies the open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It turns out that this system class inherits the relationship between controllability and stabilizability of linear systems.

Feedback linearization of piecewise linear systems

One of the classical problems of nonlinear systems and control theory is feedback linearization. Its obvious motivation is that one can utilize linear control theory if the nonlinear system at hand is linearizable by feedback. This problem is well-understood for the smooth nonlinear systems. In the present paper, we investigate feedback linearizability of a class of piecewise linear, and hence nonsmooth, systems.