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 closed-loop 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 so-called continuous-time 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 well-known classical conditions due to Hautus based on eigenvalue-based tests. This is the first time that such conditions are obtained beyond the linear case. For discrete-time conewise linear systems similar results are obtained under much more specific conditions and the non-convexity hurdle to extend the continuous-time to the full discrete-time case was revealed in one of our recent publications on the topic.

Related Publications

2017

  • On Lyapunov-Metzler inequalities and S-procedure characterisations for the stabilisation of switched linear systems

    2017
    W.P.M.H. Heemels, A. Kundu, J. Daafouz
    IEEE Transactions on Automatic Control

  • Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations

    2017
    A. Kundu, J. Daafouz, W.P.M.H. Heemels
    IFAC World Congress 2017, Toulouse, France

2016

  • 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. 38-46

  • L2-gain Analysis for a Class of Hybrid Systems with Applications to Reset and Event-triggered 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. 2766-2781

2015

  • 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, Urbana-Champaign, USA, p. 238-243

  • 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. "(IFAC-PapersOnLine, Volume 48, Issue 27, 2015)", p. 80-85

  • 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 data-processing methods for feedback control: Breaking the speed versus accuracy trade-off

    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

2013

  • Controllability of a class of bimodal discrete-time piecewise linear systems

    April, 2013
    E. Yurtseven, M.K. Camlibel, and W.P.M.H. Heemels
    Systems and Control Letters 62(4), p. 338-344

  • Further Input-to-State Stability Subtleties for Discrete-Time Systems

    June, 2013
    M. Lazar, W.P.M.H. Heemels, and A.R. Teel
    IEEE Transactions on Automatic Control 58(6), p. 1609-1613

  • Controllability of a Class of Bimodal Discrete-Time 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. 1663-1668

2012

  • 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. 69-78

  • 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. 4223-4228

  • 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. 258-263

2011

  • 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. 869-874

2010

  • 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. 6475-6480

  • Further Input-to-State Stability Subtleties for Discrete-time Systems

    September, 2010
    M. Lazar, W.P.M.H. Heemels and A.R. Teel
    UKACC International Conference on Control 2010, Coventry, UK "(invited paper)"

2009

  • Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions

    January, 2009
    M. Lazar and W.P.M.H. Heemels
    Automatica 45(1), p. 180-185

  • Lyapunov functions, stability and input-to-state stability subtleties for discrete-time discontinuous systems

    September, 2009
    M. Lazar, W.P.M.H. Heemels and A.R. Teel
    IEEE Transactions on Automatic Control 54(10), p. 2421-2425

  • 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 Theory-Tools-Applications", Cambridge University Press, p. 139-192

  • 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 Theory-Tools-Application", Cambridge University Press, p. 31-55

2008

  • 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. 762-774

  • 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. 1261-1267

  • Input-to-state stability and interconnections of discontinuous dynamical systems

    December, 2008
    W.P.M.H. Heemels and S. Weiland
    Automatica 44(12), p. 3079-3086

  • Global input-to-state stability and stabilization of discrete-time piecewise affine systems

    August, 2008
    M. Lazar and W.P.M.H. Heemels
    Nonlinear Analysis: Hybrid Systems 2(3), p. 721-734

  • On robustness of constrained discrete-time 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. 1161-1165

  • Observer-based control of discrete-time 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. 4675-4680

  • 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. 11196-1120

  • Observer-based 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. 259-272

2007

  • On interconnections of discontinuous dynamical systems: an input-to-state stability approach

    December, 2007
    W.P.M.H. Heemels and S. Weiland
    IEEE Conference on Decision and Control (CDC) 2007, New Orleans, USA, p. 109-114

  • Subtleties in stability of discrete-time 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. 3464-3469

  • Input-to-state stability of discontinuous dynamical systems with an observer-based 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. 259-272

2006

  • 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. 290-295

  • Global input-to-state stability and stabilization of discrete-time 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

  • Model Predictive Control of Hybrid Systems: Stability and Robustness

    2006
    M. Lazar
    Eindhoven University of Technology "PhD Thesis"

2004

  • 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. 250-264

2003

  • 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. 1036-1046

  • The complementarity class of hybrid dynamical systems

    2003
    W.P.M.H. Heemels and B. Brogliato
    European Journal of Control 9(2-3), p. 322-360

  • 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. 1651-1656

  • Modelling, well-posedness, 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. 249-266

2002

  • 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. 315-327

  • 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. 220-237

  • 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

2001

  • Modelling, Control and Fault Detection of Discretely-Observed Systems

    2001
    P.P.H.H. Philips
    Eindhoven University of Technology "PhD Thesis"

2000

  • 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 Time-Domain Constraints 2000, Eindhoven, The Netherlands

  • 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

1999

  • 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. 3043-3042

  • 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"