M.K. Camlibel

On the Zeno behavior of linear complementarity systems

The so-called Zeno phenomenon is addressed for linear complementarity systems which are interconnections of linear systems and complementarity conditions. We present some sufficient conditions for absence of Zeno behavior. It is also shown that the zero state, which is the most obvious candidate for being a Zeno state, cannot be a Zeno state in certain cases.

A state transfer principle for switching port-Hamiltonian systems

Instantaneous charge/flux transfers may occur in switched electrical circuits when the switch configuration changes. Characterization of such state discontinuities is a classical issue in circuit theory which, typically, is based on the so-called charge and flux conservation principle. This paper proposes a general state transfer principle for arbitrary switching port-Hamiltonian systems. This new principle coincides with the charge and flux conservation principle in the special case of linear RLC circuits, but also covers circuits with nonlinear capacitors and inductors, and of arbitrary topology. Moreover, the new principle is applied to switching mechanical systems.

On the convergence of linear passive complementarity systems

The notion of convergent systems is a powerful tool both in the analysis and synthesis of nonlinear systems. Sufficient conditions for convergence have been under investigation for smooth systems and for classes of non-smooth switching systems in the literature. In this paper, we look at a very particular class of non- smooth systems, namely complementarity systems. These systems have the capability of capturing the non-smooth dynamics of various interesting applications from different fields of engineering. The main contribution of this paper is to show that a linear complementarity system is convergent if the underlying linear dynamics possesses a certain positive realness property.

Simultaneous balancing and model reduction of switched linear systems

In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not limited to a certain type of balancing, and they are applicable for different types of balancing corresponding to different equations, like Lyapunov or Riccati equations. The results obtained are used for model order reduction of switched linear systems (SLS) by simultaneous balanced truncation. Finally, we give conditions under which global uniform exponential stability is preserved after simultaneous balanced truncation of the original switched linear system.

Incrementally port-Hamiltonian systems

This paper introduces the new class of incrementally port-Hamiltonian systems. This class can be obtained from standard port-Hamiltonian systems by replacing the composition of the Dirac structure and energy-dissipating relation by a maximal monotone relation. After introducing this new class of systems, we study their compositions and show that incrementally port-Hamiltonian systems are closed under composition. Also, we study existence and uniqueness os state trajectories for such systems as well as an energy-based state re-initialization principle.

Robust synchronization of coprime factor perturbed networks

This paper deals with robust synchronization of directed and undirected multi-agent networks with uncertain agent dynamics. Given a network with identical nominal dynamics, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. These perturbations are assumed to be stable and have H-infinity-norm that is bounded by an a priori given desired tolerance. We derive state space equations for dynamic observer based protocols that achieve robust synchronization in the presence of such uncertainty. We obtain an achievable interval, i.e. an interval such that for each value of the tolerance contained in this interval there exists a robustly synchronizing protocol

The disturbance decoupling problem for continuous piecewise affine systems

In this paper we study the disturbance decoupling problem for continuous piecewise affine systems. We establish a set of necessary conditions and a set of sufficient conditions, both geometric in nature, for such systems to be disturbance decoupled. Furthermore, we investigate mode-independent state feedback controllers for piecewise affine systems and provide sufficient conditions for the solvability of the disturbance decoupling problem by state feedback.

Fault detection and isolation for systems defined over graphs

We consider the problem of fault detection and isolation for a class of linear dynamical systems defined by a graph containing faulty vertices and observer vertices. Using a geometric approach, we provide a characterization of the smallest conditioned invariant subspaces generated by faults in terms of the underlying graph structure. Based on this characterization, we give graph-theoretic conditions guaranteeing fault detectability. In addition, we provide a condition under which fault detectability fails.

Time-stepping methods for constructing periodic solutions in maximally monotone set-valued dynamical systems

In this paper we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under certain conditions. We discuss two numerical time-stepping schemes for the computation of periodic solutions of these systems when being periodically excited. For these two schemes we will provide formal mathematical justifications and compare them in terms of approximation accuracy and computation time using a numerical example.

When is a linear multi-modal system disturbance decoupled?

In this paper we study the question under which conditions a linear multi-modal system is disturbance decoupled. We establish necessary and sufficient geometric conditions from which the existing results on switched linear systems and conewise linear systems can be recovered as special cases. Also, we apply these conditions to a class of linear complementarity systems in order to obtain a more crisp characterization.