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
-
Analysis of Sampled-Data Hybrid Integrator-Gain Systems: A
Discrete-Time Approach
2024
B. Sharif, D. Alferink, M. Heertjes, H. Nijmeijer, W.P.M.H. Heemels
Automatica
-
Scaled graphs for reset control systems
2024
S. van den Eijnden, T.L. Chaffey, T. Oomen, W.P.M.H. Heemels
European Control Conference 2024, Stockholm, Sweden
-
Stability analysis of hybrid integrator-gain systems using linear programming
2024
J.J. Palacios Roman, S. Hafstein, S. van den Eijnden, M. Heertjes, W.P.M.H. Heemels
8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
-
Stability and performance analysis of hybrid integrator-gain systems: An LMI approach
2024
S. van den Eijnden, W.P.M.H. Heemels, H. Nijmeijer, W.P.M.H. Heertjes
8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
-
Incremental Stability of Discrete-Time First-Order Projection Elements
2024
R. Bertollo, S. van den Eijnden, W.P.M.H. Heemels
8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
-
Frequency-Domain Tools for Stability Analysis of Hybrid Integrator-Gain Systems
2021
S. van den Eijnden, M. Heertjes (23277), W.P.M.H. Heemels, H. Nijmeijer
European Control Conference, Rotterdam, The Netherlands, 2021, p. 1895-1900
-
Overcoming Performance Limitations of Linear Control with Hybrid Integrator-Gain 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 "IFAC PapersOnline" 54(4), p. 289-294
-
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. 1060-1065
-
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 49, p. 37-63
-
On the graphical stability of hybrid solutions with non-matching 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 Conference on Decision and Control (CDC) 2020, Jeju Island, Republic of Korea "IEEE Control Systems Letters" 4(4), p. 1060-1065
-
Practical Stabilisation of Switched Affine Systems with Dwell-Time
Guarantees
2019
C. Albea Sanchez, G. Garcia, S. Hadjeras, W.P.M.H.
Heemels, L. Zaccarian
IEEE Transactions on Automatic Control 64(11), p. 4811-4817
-
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. 3361-3376
-
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. 4094-4109
-
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 62(9), p. 4593 - 4597
-
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 "[IFAC-PapersOnline]" 50-1, p. 3412–3417
-
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
-
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
-
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, 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
-
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
-
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 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
-
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 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
-
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)"
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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. 250-264
-
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
-
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
-
Modelling, Control and Fault Detection of Discretely-Observed Systems
2001
P.P.H.H. Philips
Eindhoven University of Technology "PhD Thesis"
-
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
-
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"