Safety Verification of Hybrid Systems Using Barrier Certificates

  • Stephen Prajna
  • Ali Jadbabaie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2993)


This paper presents a novel methodology for safety verification of hybrid systems. For proving that all trajectories of a hybrid system do not enter an unsafe region, the proposed method uses a function of state termed a barrier certificate. The zero level set of a barrier certificate separates the unsafe region from all possible trajectories starting from a given set of initial conditions, hence providing an exact proof of system safety. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes nonlinearity, uncertainty, and constraints can be handled directly within this framework. The method is also computationally tractable, since barrier certificates can be constructed using the sum of squares decomposition and semidefinite programming. Some examples are provided to illustrate the use of the method.


Hybrid System Continuous State Discrete Transition Reachability Analysis Integral Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Stephen Prajna
    • 1
  • Ali Jadbabaie
    • 2
  1. 1.Control and Dynamical SystemsCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA

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