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Dive into the research topics where Rh Rob Gielen is active.

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Featured researches published by Rh Rob Gielen.


Automatica | 2010

Technical communique: On polytopic inclusions as a modeling framework for systems with time-varying delays

Rh Rob Gielen; Sorin Olaru; M Mircea Lazar; Wpmh Maurice Heemels; van de N Nathan Wouw; S.-I. Niculescu

One of the important issues in networked control systems is the appropriate handling of the nonlinearities arising from uncertain time-varying delays. In this paper, using the Cayley-Hamilton theorem, we develop a novel method for creating discrete-time models of linear systems with time-varying input delays based on polytopic inclusions. The proposed method is compared with existing approaches in terms of conservativeness, scalability and suitability for controller synthesis.


Systems & Control Letters | 2014

An alternative converse Lyapunov theorem for discrete-time systems

Roman Geiselhart; Rh Rob Gielen; M Mircea Lazar; Fabian Wirth

Abstract This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov functions on a set [ a , b ] with 0 a b ∞ are derived. Furthermore, for specific classes of systems, the developed converse Lyapunov theorem can be used to establish non-conservatism of existence of a particular type of Lyapunov functions. Most notably, a proof that the existence of conewise linear Lyapunov functions is non-conservative for GES conewise linear systems is given and, as a by-product, tractable construction of polyhedral Lyapunov functions for linear systems is attained.


Siam Journal on Control and Optimization | 2012

Lyapunov Methods for Time-Invariant Delay Difference Inclusions

Rh Rob Gielen; M Mircea Lazar; Ilya V. Kolmanovsky

Motivated by the fact that delay difference inclusions (DDIs) form a rich modeling class that includes, for example, uncertain time-delay systems and certain types of networked control systems, this paper provides a comprehensive collection of Lyapunov methods for DDIs. First, the Lyapunov-Krasovskii approach, which is an extension of the classical Lyapunov theory to time-delay systems, is considered. It is shown that a DDI is


Automatica | 2011

Stabilization of polytopic delay difference inclusions via the Razumikhin approach

Rh Rob Gielen; M Mircea Lazar

\mathcal{KL}


conference on decision and control | 2009

Stabilization of networked control systems via non-monotone control ^lyapunov functions

Rh Rob Gielen; M Mircea Lazar

-stable if and only if it admits a Lyapunov-Krasovskii function (LKF). Second, the Lyapunov-Razumikhin method, which is a type of small-gain approach for time-delay systems, is studied. It is proved that a DDI is


advances in computing and communications | 2010

On Lyapunov theory for delay difference inclusions

Rh Rob Gielen; M Mircea Lazar; Ilya V. Kolmanovsky

\mathcal{KL}


Mathematics of Control, Signals, and Systems | 2012

Input-to-state stability analysis for interconnected difference equations with delay

Rh Rob Gielen; M Mircea Lazar; Andrew R. Teel

-stable if it admits a Lyapunov-Razumikhin function (LRF). Moreover, an example of a linear delay difference equation which is globally exponentially stable but does not admit an LRF is provided. Thus, it is established that the existence of an LRF is not a necessary condition for


conference on decision and control | 2012

Non-conservative dissipativity and small-gain conditions for stability analysis of interconnected systems

Rh Rob Gielen; M Mircea Lazar

\mathcal{KL}


Lecture Notes in Control and Information Sciences | 2009

On Polytopic Approximations of Systems with Time-Varying Input Delays

Rh Rob Gielen; Sorin Olaru; M Mircea Lazar

-stability of a DDI. Then, it is shown that the existence of an LRF is a sufficient condition for the existence of an LKF and that only under certain additional assumptions is the converse true. Furthermore, it is shown that an LRF induces a family of sets with certain contraction properties that are particular to time-delay systems. On the other hand, an LKF is shown to induce a type of contractive set similar to those induced by a classical Lyapunov function. The class of quadratic candidate functions is used to illustrate the results derived in this paper in terms of both LKFs and LRFs, respectively. Both stability analysis and stabilizing controller synthesis methods for linear DDIs are proposed.


IEEE Transactions on Automatic Control | 2013

Necessary and Sufficient Razumikhin-Type Conditions for Stability of Delay Difference Equations

Rh Rob Gielen; M Mircea Lazar; Saša V. Raković

Polytopic delay difference inclusions (DDIs) have received increasing attention recently, mostly due to their ability to model a wide variety of relevant processes, including networked control systems. One of the fundamental problems for DDIs that poses a non-trivial challenge is stabilization. This paper embraces the Razumikhin approach and provides several solutions to the stabilization problem as follows. Firstly, a method to synthesize a control Lyapunov-Razumikhin function (cLRF) is presented for unconstrained DDIs. Secondly, for constrained DDIs, a receding horizon controller based on the cLRF for the unconstrained system is proposed, along with a closed-loop stability analysis. Thirdly, it is shown that a tractable implementation of the developed control algorithm can be attained even for large delays, by means of an on-line Minkowski set addition. An advantageous feature of the developed methodology is that all the synthesis algorithms can be formulated as a low complexity semi-definite programming problem for quadratic cLRF candidates. A comparison with alternative synthesis methods demonstrates the advances provided by the developed theory.

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M Mircea Lazar

Eindhoven University of Technology

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Wpmh Maurice Heemels

Eindhoven University of Technology

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Andrew R. Teel

University of California

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Sasa V. Rakovic

Otto-von-Guericke University Magdeburg

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