Stability, Stabilizability & Controllability
In this subtheme of "Hybrid and Switched Systems" we ask ourselves the following questions:
 Stability: Under which (algebraic) conditions do hybrid systems exhibit stable behavior?
 Stabilizability:
Under which conditions can the control inputs of a hybrid system be chosen such that the resulting closedloop system becomes stable?
 Controllability:
Under which conditions can the control inputs of a hybrid system be chosen such that the we can steer the state of the system from any arbitrary initial state to any desirable final state?
Interestingly, for socalled continuoustime conewise linear systems (a class of piecewise linear system in which the regions are given by cones) we provide algebraic conditions for controllability and stabilizability that are similar in nature than the wellknown classical conditions due to Hautus based on eigenvaluebased tests. This is the first time that such conditions are obtained beyond the linear case. For discretetime conewise linear systems similar results are obtained under much more specific conditions and the nonconvexity hurdle to extend the continuoustime to the full discretetime case was revealed in one of our recent publications on the topic.
Related Publications

Overcoming Performance Limitations of Linear Control with Hybrid IntegratorGain Systems
2021
D. van Dinther, B. Sharif, S. van den Eijnden, H. Nijmeijer, M. Heertjes, W.P.M.H. Heemels
IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2021, Brussels, Belgium

FrequencyDomain Tools for Stability Analysis of Hybrid IntegratorGain Systems
2021
S. van den Eijnden, M. Heertjes (23277), W.P.M.H. Heemels, H. Nijmeijer
European Control Conference, Rotterdam, The Netherlands, 2021

To stick or to slip: A reset PID control perspective on positioning systems with friction
2020
A. Bisoffi, R. Beerens, W.P.M.H. Heemels, H. Nijmeijer, N. van de Wouw, L. Zaccarian
Annual Reviews in Control

On the graphical stability of hybrid solutions with nonmatching jump
times
2020
J.J.B. Biemond, R. Postoyan, W.P.M.H. Heemels, N. van de Wouw
Automatica, p. 108662

Oblique Projected Dynamical Systems and Incremental Stability under State Constraints
2020
W.P.M.H. Heemels, M.K. Camlibel, M. Heertjes
IEEE Control Systems Letters 4(4), p. 10601065

Oblique Projected Dynamical Systems and Incremental Stability under State Constraints
2020
W.P.M.H. Heemels, M.K. Camlibel, M. Heertjes
IEEE Conference on Decision and Control (CDC) 2020, Jeju Island, Republic of Korea

Practical Stabilisation of Switched Affine Systems with DwellTime
Guarantees
2019
C. Albea Sanchez, G. Garcia, S. Hadjeras, W.P.M.H.
Heemels, L. Zaccarian
IEEE Transactions on Automatic Control 64(11), p. 48114817

Observability and controllability analysis of linear systems subject to data losses
2018
R.M. Jungers, A. Kundu, W.P.M.H. Heemels
IEEE Transactions on Automatic Control 63(10), p. 33613376

Incremental Stability of Hybrid Dynamical Systems
2018
J.J.B. Biemond, R. Postoyan, W.P.M.H. Heemels, N. Van De Wouw
IEEE Transactions on Automatic Control 63(12), p. 40944109

On LyapunovMetzler inequalities and Sprocedure characterisations for the stabilisation of switched linear systems
2017
W.P.M.H. Heemels, A. Kundu, J. Daafouz
IEEE Transactions on Automatic Control 62(9), p. 4593  4597

Stabilization of discretetime switched linear systems: LyapunovMetzler inequalities versus Sprocedure characterizations
2017
A. Kundu, J. Daafouz, W.P.M.H. Heemels
IFAC World Congress 2017, Toulouse, France "[IFACPapersOnline]" 501, p. 3412–3417

Distance function design and Lyapunov techniques for the stability of hybrid trajectories
2016
J. J.B. Biemond, W.P.M.H. Heemels, R. Sanfelice, N. van de Wouw
Automatica 73, p. 3846

L2gain Analysis for a Class of Hybrid Systems with Applications to
Reset and Eventtriggered Control: A Lifting Approach
October, 2016
W.P.M.H. Heemels, G.E. Dullerud, A.R. Teel
IEEE Transactions on Automatic Control 61(10), p. 27662781

Definitions of incremental stability for hybrid systems (invited paper)
2015
R. Postoyan, J.J.B. Biemond, W.P.M.H. Heemels, N. Van De Wouw
IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 5544  5549

Switching dataprocessing methods for feedback control: Breaking the speed versus accuracy tradeoff
2015
E.P. van Horssen, D. Antunes, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 2313  2318

Constructing distance functions and piecewise quadratic Lyapunov functions for stability of hybrid trajectories
2015
J. J.B. Biemond, W.P.M.H. Heemels, R.G. Sanfelice, N. Van De Wouw
IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 2252  2257

On Observability in Networked Control Systems with Packet Losses
2015
R.M. Jungers, A. Kundu, W.P.M.H. Heemels
Annual Allerton Conference on Communication, Control, and
Computing 2015, UrbanaChampaign, USA, p. 238243

Controllability of Linear Systems Subject to Packet Losses
2015
R.M. Jungers and W.P.M.H. Heemels
IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2015, Atlanta, USA. "(IFACPapersOnLine, Volume 48, Issue 27, 2015)", p. 8085

Controllability of a class of bimodal discretetime piecewise linear systems
April, 2013
E. Yurtseven, M.K. Camlibel, and W.P.M.H. Heemels
Systems and Control Letters 62(4), p. 338344

Further InputtoState Stability Subtleties for DiscreteTime Systems
June, 2013
M. Lazar, W.P.M.H. Heemels, and A.R. Teel
IEEE Transactions on Automatic Control 58(6), p. 16091613

Controllability of a Class of Bimodal DiscreteTime Piecewise Linear Systems
July, 2013
E. Yurtseven, M.K. Camlibel, and W.P.M.H. Heemels
European Control Conference (ECC) 2013, Zurich, Switzerland to appear, p. 16631668

Disturbance Decoupling of Switched Linear Systems
January, 2012
E. Yurtseven, W.P.M.H. Heemels and M.K. Camlibel
Systems and Control Letters 61(1), p. 6978

Tracking control of mechanical systems with impacts
June, 2012
J.J.B. Biemond, N. Van De Wouw, W.P.M.H. Heemels and H. Nijmeijer
American Control Conference (ACC) 2012, Montreal, Canada, p. 258263

Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts
December, 2012
J.J.B. Biemond, N. van De Wouw, W.P.M.H. Heemels, R.G. Sanfelice, and H. Nijmeijer
IEEE Conference on Decision and Control (CDC) 2012, Hawaii, USA, p. 42234228

Tracking Control for Hybrid Systems via Embedding of Known Reference Trajectories
June, 2011
R.G. Sanfelice, J.J.B. Biemond, N. van de Wouw, and W.P.M.H. Heemels
American Control Conference (ACC) 2011, San Francisco, USA, p. 869874

Further InputtoState Stability Subtleties for Discretetime Systems
September, 2010
M. Lazar, W.P.M.H. Heemels and A.R. Teel
UKACC International Conference on Control 2010, Coventry, UK "(invited paper)"

Disturbance Decoupling of Switched Linear Systems
December, 2010
E. Yurtseven, W.P.M.H. Heemels and M.K. Camlibel
IEEE Conference on Decision and Control (CDC) 2010, Atlanta, USA, p. 64756480

Predictive control of hybrid systems: Inputtostate stability results for suboptimal solutions
January, 2009
M. Lazar and W.P.M.H. Heemels
Automatica 45(1), p. 180185

Lyapunov functions, stability and inputtostate stability subtleties for discretetime discontinuous systems
September, 2009
M. Lazar, W.P.M.H. Heemels and A.R. Teel
IEEE Transactions on Automatic Control 54(10), p. 24212425

Chapter 2: Survey of modelling, analysis and control of hybrid systems
2009
B. De Schutter, W.P.M.H. Heemels, J. Lunze and C. Prieur
in "HYCON Handbook of Hybrid Systems Control TheoryToolsApplication", Cambridge University Press, p. 3155

Chapter 5: Further switched systems
2009
A. Bemporad, M.K. Camlibel, W.P.M.H. Heemels, A. J. van der Schaft, J.M. Schumacher and B. De Schutter
in "HYCON Handbook of Hybrid Systems Control TheoryToolsApplications", Cambridge University Press, p. 139192

Inputtostate stability and interconnections of discontinuous dynamical systems
December, 2008
W.P.M.H. Heemels and S. Weiland
Automatica 44(12), p. 30793086

Global inputtostate stability and stabilization of discretetime piecewise affine systems
August, 2008
M. Lazar and W.P.M.H. Heemels
Nonlinear Analysis: Hybrid Systems 2(3), p. 721734

On robustness of constrained discretetime systems to state measurement errors
April, 2008
B.J.P. Roset, W.P.M.H. Heemels, M. Lazar and H. Nijmeijer
Automatica 44(4), p. 11611165

Algebraic necessary and sufficient conditions for the controllability of conewise linear systems
April, 2008
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
IEEE Transactions on Automatic Control 53(3), p. 762774

A full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs
May, 2008
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
Automatica 44(5), p. 12611267

Observerbased control of discretetime piecewise affine systems: Exploiting continuity twice
December, 2008
W.P.M.H. Heemels, M. Lazar, N. van de Wouw and A.V. Pavlov
IEEE Conference on Decision and Control (CDC) 2008, Cancun, Mexico, p. 46754680

Predictive control of hybrid systems: Stability results for suboptimal solutions
July, 2008
M. Lazar and W.P.M.H. Heemels
IFAC World Congress 2008, Seoul, Korea, p. 111961120

Observerbased control of linear complementarity systems
2008
W.P.M.H. Heemels, M.K. Camlibel, B. Brogliato and J.M. Schumacher
in "Lecture Notes in Computer Science. 11th International Workshop on Hybrid Systems: Computation and Control 2008", Springer, p. 259272

Subtleties in stability of discretetime piecewise affine systems
June, 2007
M. Lazar, W.P.M.H. Heemels and A.R. Teel
American Control Conference (ACC) 2007, New York, USA, p. 34643469

On interconnections of discontinuous dynamical systems: an inputtostate stability approach
December, 2007
W.P.M.H. Heemels and S. Weiland
IEEE Conference on Decision and Control (CDC) 2007, New Orleans, USA, p. 109114

Inputtostate stability of discontinuous dynamical systems with an observerbased control application
2007
W.P.M.H. Heemels, S. Weiland and A.Lj. Juloski
in "Lecture Notes in Computer Science. 10th International Workshop on Hybrid Systems: Computation and Control 2007, Pisa, Italy", Springer, p. 259272

Global inputtostate stability and stabilization of discretetime piecewise affine uncertain systems
June, 2006
M. Lazar and W.P.M.H. Heemels
IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2006, Alghero, Italy

Stabilizability of bimodal piecewise linear systems with continuous vector field
June, 2006
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2006, Alghero, Italy, p. 290295

Model Predictive Control of Hybrid Systems: Stability and Robustness
2006
M. Lazar
Eindhoven University of Technology "PhD Thesis"

On the controllability of bimodal piecewise linear systems
2004
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
in "Hybrid Systems: Computation and Control, LNCS", Springer 2993, p. 250264

Switched networks and complementarity
August, 2003
M.K. Camlibel, W.P.M.H. Heemels, A.J. van der Schaft and J.M. Schumacher
IEEE Transactions on Circuits and Systems "I: Fundamental Theory and Applications" 50(8), p. 10361046

The complementarity class of hybrid dynamical systems
2003
W.P.M.H. Heemels and B. Brogliato
European Journal of Control 9(23), p. 322360

Stability and controllability of bimodal planar linear complementarity systems
December, 2003
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
IEEE Conference on Decision and Control (CDC) 2003, Hawaii, USA, p. 16511656

Modelling, wellposedness, and stability of switched electrical networks
2003
W.P.M.H. Heemels, M.K. Camlibel, A.J. van der Schaft and J.M. Schumacher
in "Hybrid Systems: Computation and Control, Lecture Notes in Computer Science", Springer 2623, p. 249266

On the dynamic analysis of piecewise linear networks
March, 2002
W.P.M.H. Heemels, M.K. Camlibel and J.M. Schumacher
IEEE Transactions on Circuits and Systems "I: Fundamental Theory and Applications" 49(3), p. 315327

On linear passive complementarity systems
2002
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
European Journal of Control 8(3), p. 220237

On switched Hamiltonian systems
2002
K.M. Gerritsen, A.J. van der Schaft and W.P.M.H. Heemels
International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2002, South Bend, USA

Modelling, Control and Fault Detection of DiscretelyObserved Systems
2001
P.P.H.H. Philips
Eindhoven University of Technology "PhD Thesis"

On dynamics, complementarity and passivity: electrical networks with ideal diodes
2000
W.P.M.H. Heemels, M.K. Camlibel and J.M. Schumacher
Conference on Automation of Mixed Processes: Hybrid Dynamic Systems 2000, Dortmund, Germany

Continuity of smooth approximations of complementarity systems
2000
M.K. Camlibel, M.K.K. Cevik, W.P.M.H. Heemels and J.M. Schumacher
Workshop on Systems with TimeDomain Constraints 2000, Eindhoven, The Netherlands

The nature of solutions to linear passive complementarity systems
December, 1999
M.K. Camlibel, W.P.M.H. Heemels and J.M. Schumacher
IEEE Conference on Decision and Control (CDC) 1999, Phoenix, USA, p. 30433042

Linear complementarity systems: a study in hybrid systems
1999
W.P.M.H. Heemels (supervised by Hans Schumacher, Siep Weiland and Paul van den Bosch)
Eindhoven University of Technology "PhD Thesis"