Dynamical properties of hybrid automata

Lygeros, John; Johansson, Karl Henrik; Simić, Slobodan N.; Zhang, Jun; Sastry, S. Shankar

doi:10.1109/tac.2002.806650

Cited by 686 publications

(511 citation statements)

References 45 publications

(58 reference statements)

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“…This model easily fits into standard modeling frameworks for hybrid systems (see, e.g., [10,6,11]), and the reader can consult these references for background and further technical details. The description to be provided here is somewhat informal, but it is sufficient for presenting the results.…”

Section: Hybrid System Modelmentioning

confidence: 99%

“…Since V 1 and V 2 are positive definite and radially unbounded, there exist functions α 1,x , α 2,x , α 1,µ , α 2,µ ∈ K ∞ such that (6) and (8) hold. Using (22), (24), and (32), we obtain…”

Section: Theoremmentioning

confidence: 99%

“…In this paper, we present a novel construction of a Lyapunov function for a class of hybrid systems satisfying the conditions of the ISS small-gain theorem. We also describe another approach, based on constructing a weak (non-strictly decreasing) Lyapunov function and applying the LaSalle invariance principle for hybrid systems from [6]. We note that while the basic idea of the small-gain stability analysis for hybrid systems was announced and initially examined by the authors in [7], the Lyapunov function constructions are reported here for the first time and represent the main technical contribution of this work.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Hybrid Systems Via Small-Gain Theorems

Liberzon

Nešić

2006

Hybrid Systems: Computation and Control

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Abstract. We present a general approach to analyzing stability of hybrid systems, based on input-to-state stability (ISS) and small-gain theorems. We demonstrate that the ISS small-gain analysis framework is very naturally applicable in the context of hybrid systems. Novel Lyapunovbased and LaSalle-based small-gain theorems for hybrid systems are presented. An illustrative application of the proposed approach in the context of a quantized feedback control problem is treated in detail. The reader does not need to be familiar with ISS or small-gain theorems to be able to follow the paper.

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Section: Hybrid System Modelmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Hybrid Systems Via Small-Gain Theorems

Liberzon

Nešić

2006

Hybrid Systems: Computation and Control

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“…A fair amount of research has been done on the modeling of hybrid systems [1,3,10,12,31,32,39,43,49,51], but most of this work concentrated on deterministic systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

132

122

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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for Piecewise-Deterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.

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“…The proof of this result uses standard arguments from hybrid systems theory, see for instance [7], and is therefore omitted.…”

Section: Continuous Dynamicsmentioning

confidence: 99%

Controller design under safety specifications for a class of bounded hybrid automata

Hoehener

Vecchio

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Motivated by driver-assist systems that warn the driver before taking control action, we study the safety problem for a class of bounded hybrid automata. We show that for this class there exists a least restrictive safe feedback controller that has a simple structure and can be computed efficiently online. The theoretical results are then used to design driver-assist systems for rear-end and merging collision scenarios.

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Dynamical properties of hybrid automata

Cited by 686 publications

References 45 publications

Stability Analysis of Hybrid Systems Via Small-Gain Theorems

Stability Analysis of Hybrid Systems Via Small-Gain Theorems

Stochastic Hybrid Systems: Application to Communication Networks

Controller design under safety specifications for a class of bounded hybrid automata

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