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The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewiselinear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 685 (12 self)
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A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied
Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
, 1992
"... We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many of the examp ..."
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Cited by 460 (20 self)
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of the examples considered in the workshop can be defined by hybrid automata. While the reachability problem is undecidable even for very restricted classes of hybrid automata, we present two semidecision procedures for verifying safety properties of piecewiselinear hybrid automata, in which all variables change
HyTech: A Model Checker for Hybrid Systems
 Software Tools for Technology Transfer
, 1997
"... A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing conti ..."
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Cited by 473 (6 self)
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for which a linear hybrid automaton satisfies a temporallogic requirement. 1 Introduction A hybrid system typically consists of a collection of digital programs that interact with each other and with an analog environment. Examples of hybrid systems include manufacturing controllers, automotive and flight
What's Decidable about Hybrid Automata?
 Journal of Computer and System Sciences
, 1995
"... . Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify a boundar ..."
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Cited by 377 (16 self)
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boundary between decidability and undecidability for the reachability problem of hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow independent trajectories within piecewiselinear
A Controllability Result for PiecewiseLinear Hybrid Systems Luc
, 2001
"... A piecewiselinear hybrid system is a dynamic system which is the product of a finitestate automaton and a family of affine systems on polytopes. In full generality, determination of the controllability of such systems is undecidable. For control synthesis it is therefore of interest to determine s ..."
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Cited by 8 (1 self)
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A piecewiselinear hybrid system is a dynamic system which is the product of a finitestate automaton and a family of affine systems on polytopes. In full generality, determination of the controllability of such systems is undecidable. For control synthesis it is therefore of interest to determine
Approximate Reachability Analysis of PiecewiseLinear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 140 (31 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much
Control of PiecewiseLinear Hybrid Systems on Simplices and Rectangles
, 2001
"... A necessary and sucient condition for the reachability of a piecewiselinear hybrid system is formulated in terms of reachability of a finitestate discreteevent system and of a finite family of affine systems on a polyhedral set. As a subproblem, the reachability of an affine system on a polyt ..."
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Cited by 30 (3 self)
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A necessary and sucient condition for the reachability of a piecewiselinear hybrid system is formulated in terms of reachability of a finitestate discreteevent system and of a finite family of affine systems on a polyhedral set. As a subproblem, the reachability of an affine system on a
Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems
 IEEE Transactions on Automatic Control
, 1998
"... . This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the cir ..."
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Cited by 259 (4 self)
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. This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear timeinvariant feedback, this approach yields
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