Stability of Markov jump systems with quadratic terms and its application to RLC circuits

The paper presents results for the second moment stability of continuous-time Markov jump systems with quadratic terms, aiming for engineering applications. Quadratic terms stem from physical constraints in applications, as in electronic circuits based on resistor (R), inductor (L), and capacitor (C). In the paper, an RLC circuit supplied a load driven by jumps produced by a Markov chain—the RLC circuit used sensors that measured the quadratic of electrical currents and voltages. Our result was then used to design a stabilizing controller for the RLC circuit with measurements based on that quadratic terms. The experimental data confirm the usefulness of our approach.Peer ReviewedPostprint (author's final draft

Extended balancing of continuous LTI systems:A structure-preserving approach

In this paper, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower-dimensional electrical circuit

Stability of attitude control systems acted upon by random perturbations

Mathematical models on stability of attitude control systems acted upon by random perturbation processe

Complementarity methods in the analysis of piecewise linear dynamical systems

The main object of this thesis is a class of piecewise linear dynamical systems that are related both to system theory and to mathematical programming. The dynamical systems in this class are known as complementarity systems. With regard to these nonlinear and nonsmooth dynamical systems, the research in the thesis concentrates on two themes: well-posedness and approximations. The well-posedness issue, in the sense of existence and uniqueness of solutions, is of considerable importance from a model validation point of view. In the thesis, sufficient conditions are established for the well-posedness of complementarity systems. Furthermore, an investigation is made of the convergence of approximations of these systems with an eye towards simulation

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science