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Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach

Marc Jungers, Antoine Girard, Mirko Fiacchini
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  
This paper addresses the issue of stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite  ...  Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed.  ...  Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach Marc Jungers, Antoine Girard and Mirko Fiacchini Abstract-This paper addresses the  ... 
doi:10.1109/cdc.2016.7799120 dblp:conf/cdc/JungersGF16 fatcat:jiuz7yzf4zhbnlro23t4ycyf4a

Hybrid Systems: Review and Recent Progress [chapter]

Panos J. Antsaklis, Xenofon D. Koutsoukos
2004 Software-Enabled Control  
An important special case is a linear hybrid automaton, in which the rates of change of the continuous variables are constant.  ...  The final topic discussed in the chapter is the approximation of a continuous-time system by a discrete-event system (DES). The controller can then also be a DES.  ...  Non-quadratic Lyapunov functions have also been used for studying the stability of switched linear systems [26] .  ... 
doi:10.1002/047172288x.ch14 fatcat:zjcsv5wcczcstleqzh6tgcgime

Converse Lyapunov theorems for discrete-time linear switching systems with regular switching sequences [article]

Matthew Philippe, Raphaël M. Jungers
2014 arXiv   pre-print
We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language.  ...  As a corollary of our results, we formulate an arbitrary accurate approximation scheme for estimating the asymptotic growth rate of switching systems with constrained switching sequences.  ...  A discrete-time linear switching system is a switching system where each mode is represented by a linear difference equation.  ... 
arXiv:1410.7197v3 fatcat:tbybcnczczasha6mk3jc247dly

Stability Criteria for Switched and Hybrid Systems

Robert Shorten, Fabian Wirth, Oliver Mason, Kai Wulff, Christopher King
2007 SIAM Review  
We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions.  ...  We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws.  ...  While the latter approach is difficult for general time-varying linear systems, the explicit form of the solution to (5.1) makes such an approach possible in the case of switched linear systems and gives  ... 
doi:10.1137/05063516x fatcat:wf2hfl3x5rdzngmkhmb77rozyi

Path-complete p-dominant switching linear systems [article]

Guillaume O. Berger, Fulvio Forni, Raphaël M. Jungers
2018 arXiv   pre-print
The notion of path-complete p-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems.  ...  An algorithm for deciding the path-dominance of a given system is presented.  ...  The use of path-complete Lyapunov functions has become standard in the stability analysis of (constrained) switching linear systems [7] , [6] .  ... 
arXiv:1808.09757v1 fatcat:mj32taepgbc7nlzm5io2jkgd4u

Modal occupation measures and LMI relaxations for nonlinear switched systems control [article]

Mathieu Claeys, Jamal Daafouz, Didier Henrion
2014 arXiv   pre-print
This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence.  ...  Because of the special structure of switched systems, we obtain a much more efficient method than could be achieved by applying standard moment/SOS LMI hierarchies for general optimal control problems.  ...  The second category collects extensions of the performance indices H 2 and H ∞ originally developed for linear time invariant systems without switching, and use the flexibility of Lyapunov's approach,  ... 
arXiv:1404.4699v2 fatcat:bhqpakb4hrarvccymummiixnja

2021 Index IEEE Transactions on Systems, Man, and Cybernetics: Systems Vol. 51

2021 IEEE Transactions on Systems, Man & Cybernetics. Systems  
The primary entry includes the coauthors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination.  ...  ., +, TSMC June 2021 3392-3400 Improved Stability Criteria for Discrete-Time Switched T-S Fuzzy Systems.  ...  ., +, TSMC Oct. 2021 6445-6456 Improved Stability Criteria for Discrete-Time Switched T-S Fuzzy Systems.  ... 
doi:10.1109/tsmc.2021.3136054 fatcat:b5hcsfwjw5hllpenqmaq6wpke4

Modal occupation measures and LMI relaxations for nonlinear switched systems control

Mathieu Claeys, Jamal Daafouz, Didier Henrion
2016 Automatica  
This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence.  ...  Because of the special structure of switched systems, we obtain a much more efficient method than could be achieved by applying standard moment/SOS LMI hierarchies for general optimal control problems.  ...  The second category collects extensions of the performance indices H 2 and H ∞ originally developed for linear time invariant systems without switching, and use the flexibility of Lyapunov's approach,  ... 
doi:10.1016/j.automatica.2015.11.003 fatcat:5hz4wcwlkfe45p7p6i5c7swrly

2021 Index IEEE Transactions on Fuzzy Systems Vol. 29

2021 IEEE transactions on fuzzy systems  
The primary entry includes the coauthors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination.  ...  : An LMI Approach".  ...  Con-trol for Nonlinear Large-Scale Systems: An LMI Approach".  ... 
doi:10.1109/tfuzz.2021.3134727 fatcat:m66dl6wxdbgendhdx4bliy6nky

2009 Index IEEE Transactions on Automatic Control Vol. 54

2009 IEEE Transactions on Automatic Control  
., +, TAC May 2009 938-951 Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach. Lu, J.  ...  Fu, M., +, TAC May 2009 1165-1170 Flatness of Switched Linear Discrete-Time Systems.  ...  ., +, 1723 -1727 Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System. 1881 -1886 The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric  ... 
doi:10.1109/tac.2009.2037798 fatcat:4ilhkzss6jc63ersjzi47hiwgu

Hybrid Dynamical Systems: An Introduction to Control and Verification

Lin Hai
2014 Foundations and Trends® in Systems and Control  
The financial supports of NSF-CNS-1239222 and NSF-CAREER-1253488 for this work are greatly acknowledged.  ...  Then, stability checking for the arbitrary switching linear systems can be performed by solving certain LMIs.  ...  For robust stabilization of polytopic uncertain switched linear systems, a quadratic stabilizing switching law was designed based on LMI techniques in [Zhai et al., 2003] .  ... 
doi:10.1561/2600000001 fatcat:kxr4yc3rjzet7kwzz7pcm6a2ri

Fourth special issue on linear systems and control

V.D. Blondel, D. Hinrichsen, J. Rosenthal, P. Van Dooren
2002 Linear Algebra and its Applications  
∞ -control of linear state-delay descriptor systems: an LMI approach by E.  ...  of real matrices. • Root counting, phase unwrapping, stability and stabilization of discrete time systems by L.H.  ... 
doi:10.1016/s0024-3795(02)00309-9 fatcat:uccrbt5drjfq3awgstlpbg5uba

Control systems engineering

1986 Microprocessors and microsystems  
Our research has been focused on the design of an output-based discrete-time sliding mode controller based on a linear state-space representation of the system.  ...  An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models.  ... 
doi:10.1016/0141-9331(86)90308-x fatcat:z4rjfal2uja3dnt3ptvvmk6buq

Control Systems Engineering [chapter]

2010 Controlling Uncertainty  
Our research has been focused on the design of an output-based discrete-time sliding mode controller based on a linear state-space representation of the system.  ...  An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models.  ... 
doi:10.1002/9781444328226.ch3 fatcat:vbg2pm3qang3ricvbfo65rlgdq

Black-box stability analysis of hybrid systems with sample-based multiple Lyapunov functions [article]

Adrien Banse, Zheming Wang, Raphaël M. Jungers
2022 arXiv   pre-print
We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear  ...  systems whose switching signal is constrained by an automaton.  ...  We consider data-driven stability analysis of discrete-time switching linear systems. Dynamics of a switching linear system defined by a set of matrices Σ = {A i } i∈{1,...  ... 
arXiv:2205.00699v1 fatcat:b5ye6fshlnezfjnjuhqx35uima
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