
Research Publications
This page classifies and
lists landmark research literature that is considered to be of
interest to the hybrid systems community. This is by no means intended
to be complete, just an interesting starting point. Please send me
email if there are articles
missing that should be included, preferably material that is available on the
Web.
Books
 Arjan van der Schaft and Hans Schumacher

An Introduction to Hybrid Dynamical Systems., Lecture Notes in Control and Information
Sciences 251, 2000.
Introductory text that takes stock of a number of developments in the hybrid
dynamic systems field and describes these from a more
unified point of view without trying to be encyclopaedic.
Topics include: (i) Modeling of hybrid systems, (ii) Examples of hybrid dynamical systems,
(iii) Variablestructure systems,
(iv) Complementarity systems, (v) Analysis of hybrid systems, and (vi) Hybrid control design.
Overview Articles
 Stefan Kowalewski, Martin Fritz, Holger
Graf, Jörg Preußig, Silke Simon, Olaf Stursberg, and Heinz Treseler,

A
Case Study in ToolAided Analysis of Discretely Controlled Continuous Systems:
the Two Tanks Problem", in Proceedings of the 5th Int. Workshop
on Hybrid Systems, Notre Dame, USA, September 1997.
This case study compares eight computer tools, six simulation packages
(Taylor's MATLABbased simulator, SMULINK/STATEFLOW, GPROMS, SHIFT, DYMOLA, BASIP) and two
verification tools (SMV, HYTECH), with respect to the validation of a single process control
example with nontrivial continuous dynamics.
A postscript version is available.
 R. Alur,
 Timed Automata.
In NATOASI 1998 Summer School on Verification of Digital and Hybrid Systems, 1998.
A revised and shorter version appears
in 11th International Conference on ComputerAided Verification, LNCS 1633, pp. 822,
SpringerVerlag, 1999.
A postscript version is available.
 Thomas A. Henzinger,
 The
theory of hybrid automata,
in Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (LICS 1996),
pp. 278292, 1996.
A postscript version is available.
 Pieter J. Mosterman,
 An Overview of Hybrid Simulation
Phenomena and Their Support by Simulation Packages, in Hybrid Systems: Computation and Control '99,
Lecture Notes in Computer Science vol. 1569, Frits W. Vaandrager and Jan H. van Schuppen (eds.), pp. 165177, 1999.
A postscript version is available.
 D.A. van Beek and J.E. Rooda,
 Languages and applications in hybrid modelling
and simulation: Positioning of Chi, in Control Engineering Practice, vol. 8, nr. 1, 2000, pp. 8191.
A pdf version is available.
 John Lygeros, George J. Pappas, and Shankar Sastry,
 An introduction to hybrid systems modeling, analysis and control,
in Preprints of the First Nonlinear Control Network Pedagogical School, pages 307329, Athens, Greece, 1999.
A postscript version is available.
Modeling
 Maurice Heemels,

Linear Complementarity Systems: A Study in Hybrid Dynamics,
Ph.D. Thesis, Eindhoven University of Technology, Netherlands, 1999.
Examples of socalled "complementarity systems" are mechanical systems subject
to inequality constraints and consequently, impact phenomena. The characterizing ingredients of
complementarity systems are differential equations in conjunction with complementarity conditions
(like ideal diode characteristics) consisting of inequalities and Boolean expressions. The complementarity
conditions are imposed on a pair of variables (u,y) in the sense that u is nonnegative, y is nonnegative
and {u=0 or y=0}.
 Georgina Fábián,

A Language and Simulator for Hybrid Systems,
Ph.D. Thesis, Eindhoven University of Technology, Netherlands, 1999.
The hybrid Chi language semantics is specified. A hybrid model simulator is
developed that integrates a nonlinear equation solver for the initial state and a DAE solver for
continuous behavior. Composition of continuous models uses channels that have the semantics of
algebraic equations. Combined with the use of local process variables this contributes significantly
to clear and robust models.
 Krister Edström,

Switched Bond Graphs: Simulation and Analysis,
Ph.D. Thesis, Linköping University, Sweden, 1999.
Algorithms for causality propagation, equation generation, and simulation
are derived. An efficient algorithm is presented, that detects causality problems like algebraic
loops, and derivative and conflicting causality. It is shown that a class of classical bond graphs
can be expressed in state space form, by a variable transformation, and that correct initial
values of the continuous state variables are achieved when a new mode is entered.
 Emanuele Carpanzano,

A Development Methodology for Hybrid Control Systems,
Ph.D. Thesis, Politecnico di Milano, 1998.
 Pieter J. Mosterman,

Hybrid
Dynamic Systems: A hybrid bond graph modeling paradigm and its application in diagnosis,
Ph.D. Thesis, Vanderbilt University, 1997.
This thesis develops a formal hybrid modeling theory based on physical principles,
a model verification method, and a physically correct behavior generation algorithm.
A postscript version is available.
 M. Otter, C. Schlegel, and H. Elmqvist,

"Modeling and Realtime simulation
of an Automatic Gearbox using Modelica",
in Proceedings of ESS'97, pp. 115121, October 1922, Passau, Germany, 1997.
The automatic gearbox consists of 6 switching elements (clutches and
freewheels) leading to 64 possible configurations. It is shown how a
consistent configuration can be found in realtime after a gearshift occurred
(i.e., event iteration is adapted for realtime applications).
A postscript version is available.
 Friedrich Pfeiffer and Christoph Glocker,

Multibody Dynamics with Unilateral Contacts,
John Wiley and Sons, Inc., 1996.
This book contains new research results of the modeling of mechanical
systems with friction and impact. The basic approach consists of
transforming the problem into a complementary problem that is
solved by standard algorithms. Several applications are discussed.
 C. Majer, W. Marquardt, and E.D. Gilles,

"Reinitialization
of DAEs after Discontinuities",
Computers and Chemical Engineering, vol. 19, suppl. S507S512, 1995.
Discusses the reinitialization of DAEs with discontinuities by
solving nonlinear consistency equations.
 M. Andersson,

ObjectOriented Modelling and Simulation
of Hybrid Systems, Ph.D thesis, Lund Institute of Technology, ISRN
UTFD2/TFRT1043SE, 1994. Objectoriented models
of physical systems are transformed into a system of DAEs. A special discrete
operator allows the Grafcet method to model the discrete behavior. Event
detection and rootfinding are discussed.
 H. Elmqvist, F.E. Cellier, and M. Otter,

"ObjectOriented
Modelling of PowerElectronic Circuits Using Dymola",
in Proceedings of CISS'94, pp. 156161, August 2225, Zürich, Switzerland, 1994.
Describes how to model and simulate powerelectronic circuits with many ideal switches.
Shows that a simulation speedup of 20 can be obtained with regards to conventional methods.
A postscript version is available.
 H. Elmqvist, F.E. Cellier, and M. Otter,

"ObjectOriented
Modelling of Hybrid Systems",
in Proceedings of ESS'93, pp. xxxixli, October 2528, Delft, Netherlands, 1993.
Introduces higher level elements to describe discrete components. Uses
BLT partitioning to order these elements in order that the component equations
are evaluated in the correct order at event instants.
Introduces event iteration as an alternative to the transformation
of a complementary problem. Method is demonstrated at a system with
coupled friction elements.
A postscript version is available.
 P.I. Barton,

The
Modelling and Simulation of Combined Discrete/Continuous Processes,
Ph.D. Thesis, University of London, 1992. In this
thesis hybrid process engineering systems are modeled by DAEs for the continuous
part and by sets of finite automatas for the discrete part of physical
models.
A postscript version is available.
 H.B. Armstrong,

Control of Machines with Friction,
Kluwer Academic Publishers, 1991.
One of the rare books about friction modeling for dynamic system analysis and
design.
 P. Lötstedt,

"Coulomb Friction in TwoDimensional Rigid Body Systems",
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM),
vol. 61, pp. 605615, 1981.
This is a classical paper about hybrid mechanical systems. It shows that
even for simple mechanical systems the problem specification may lead to
a model with no (unique) solution.
Simulation
 P.I. Barton and T. Park,

"State
Event Location in DifferentialAlgebraic Models",
ACM Transactions on Modelling and Computer Simulation, vol. 6, no. 2, pp. 137165, 1996.
New results on state event location of DAE solvers.
A postscript version is available.
 E. Eich,

Projizierende Mehrschrittverfahren zur numerischen Lösung
von Bewegungsgleichungen technischer Mehrkörpersysteme mit Zwangsbedingungen und Unstetigkeiten,
Dissertation, VDIFortschrittBerichte, Reihe 18, Nr. 109, VDIVerlag, Düsseldorf, 1992.
Simulation of hybrid DAEs with projection methods.
 François E. Cellier,

Combined
Continuous/Discrete System Simulation by Use of Digital Computers: Techniques
and Tools, Ph.D. Thesis, Swiss Federal Institute of Technology,
ETH Zürich, Switzerland, 1979.
Verification
 Mayank B. Amin,

Stabilization and SubOptimal Wavelets Control of
Hybrid Dynamical Systems, Ph.D. Dissertation, University of Minnesota, 1999.
 Stefan Pettersson,

Analysis
and Design of Hybrid Systems, Ph.D. Dissertation, Chalmers University of Technology,
June, 1999. It is shown that hybrid systems can be constructed by
modular decompositions and hybrid system stability results are presented that are extensions
of Lyapunov theory applying an abstract energy function satisfying certain
properties. The search for such functions can be formulated as linear matrix inequality (LMI) problems,
amenable to computerized methods. It also addresses stability robustness (i.e., stability despite the presence
of model uncertainties) and how to switch between different continuous vector
fields guaranteeing stability of the closedloop system.
 Gerardo Lafferriere, George J. Pappas, and Sergio Yovine

"Decidable
Hybrid Systems", in KIT Workshop on Verification of Hybrid Systems , October 1921, Grenoble, France,
1998. This paper extends the decidability frontier for classes of
linear hybrid systems, those with
linear vector fields in each discrete location. It shows that such hybrid systems
admit a finite bisimulation, and presents an algorithm that
computes it using decision methods from mathematical logic.
 R. Alur and D. Dill,

"A theory of timed automata",
Theoretical Computer Science, 126, pp. 183235,
1994. In this paper timed automata are introduced.
 T.A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine,

"Symbolic model checking for realtime
systems", Information and Computation, 111, pp. 193244, 1994.
In this paper, a (branching) realtime temporal logic is introduced.
 R. Alur, T.A. Henzinger, and P.H. Ho,

"Automatic symbolic verification of
embedded systems". A preliminary version of the paper appeared in Proceedings
RTSS '93, pp. 211, IEEE Computer Society Press, 1993. In
this paper the model of timed automata is generalized to linear hybrid
automata.
 Vineet Gupta, Radha Jagadeesan, Vijay A. Saraswat,

"Hybrid
CC, Hybrid Automata and Program Verification",
Proceedings of Hybrid Systems III, edited by Alur, Henzinger and
Sontag, LNCS 1066, Springer Verlag. Demonstrates
the relationship of Hybrid CC to the methodology and tools developed in
the research on verification of hybrid systems.
A postscript version is available.
 Rajeev Alur, Costas Courcoubetis, Thomas
A. Henzinger, Nicolas Halbwachs, PeiHsin Ho, Xavier Nicollin, Alfredo
Olivero, Joseph Sifakis, and Sergio Yovine,

"The
Algorithmic Analysis of Hybrid Systems", Theoretical Computer Science,
to appear. Presents a general framework for
the formal specification and algorithmic analysis of linear hybrid systems.
Hybrid systems are modeled as finite automata equipped with variables that
evolve continuously with time.
A postscript version is available.
Specification
 P.J.L. Cuijpers and M.A. Reniers,

Hybrid process algebra,
Computer Science Report, Eindhoven University of Technology, 2003.
A pdf version is available.
 Jennifer M. Davoren,

Modal
Logics for Continuous Dynamics,
Ph.D. Thesis, Department of Mathematics, Cornell University, 1998.
This work is a formal investigation of a number of bimodal and
polymodal logics built on a base of propositional S4, and is a contribution
to the theory of hybrid control systems.
A postscript version is available.
 Moshe Gotesman,

Modeling of Hybrid Dynamic Systems,
Ph.D. Thesis, Texas Tech University, 1996.
Presents a technique for converting a mathematical or
block diagram representation of a hybrid dynamic system into a Hybrid Dynamics
Petri Net (HDPN) and vice versa. It also demonstrates the modeling power of
Petri nets for nonlinear and MIMO systems.
 VV. Friesen,

"An
Exercise in Hybrid System Specification Using an Extension of Z", in
Second European Workshop on RealTime and Hybrid Systems, A. Bouajjani
and O. Maler, editors, pp. 311316, 1995.Illustrates
the main concepts of ZimOO, an extended subset of ObjectZ to describe
continuous and discrete features by a common formalism.
A postscript version is available.
 Vineet Gupta, Radha Jagadeesan, Vijay
A. Saraswat, Danny G. Bobrow,

"Programming
in Hybrid Constraint Languages", Hybrid Systems II, LNCS 999,
Springer Verlag, 1994. Presents a declarative language
for modeling hybrid systems compositionally. Programs are understood as
logical formulas that place constraints upon the temporal evolution of
a system.
A postscript version is available.
