Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
A game-theoretic approach to hybrid system design
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Interconnected automata and linear systems: a theoretical framework in discrete-time
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Studies in hybrid systems: modeling, analysis, and control
Studies in hybrid systems: modeling, analysis, and control
Integration Graphs: A Class of Decidable Hybrid Systems
Hybrid Systems
Hybrid Control for Automotive Engine Management: The Cut-Off Case
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Verification of Hybrid Systems via Mathematical Programming
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Complexity of stability and controllability of elementary hybrid systems
Automatica (Journal of IFAC)
Propositional logic in control and monitoring problems
Automatica (Journal of IFAC)
A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
On the Optimal Control Law for Linear Discrete Time Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Analysis of Discrete-Time PWA Systems with Logic States
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Primal–dual tests for safety and reachability
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Brief Analysis of discrete-time piecewise affine and hybrid systems
Automatica (Journal of IFAC)
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
Identification of piecewise affine systems via mixed-integer programming
Automatica (Journal of IFAC)
One-shot computation of reachable sets for differential games
Proceedings of the 16th international conference on Hybrid systems: computation and control
| Hi-index | 0.01 |
In this paper, we formulate the problem of characterizing the stability of a piecewise affine (PWA) system as a verification problem. The basic idea is to take the whole IRn as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semi-global stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as "asymptotically stable in T steps" the trajectories that enter an invariant set around the origin within a finite time T, or as "unstable in T steps" the trajectories which enter a set Xinst of (very large) states. Subsets of X(0) leading to none of the two previous cases are labeled as "non-classifiable in T steps". The domain of asymptotical stability in T steps is a subset of the domain of attraction of an equilibrium point, and has the practical meaning of collecting the initial conditions from which the settling time to a specified set around the origin is smaller than T. In addition, it can be computed algorithmically in finite time. Such an algorithm requires the computation of reach sets, in a similar fashion as what has been proposed for verification of hybrid systems. In this paper we present a substantial extension of the verification algorithm presented in [6] for stability characterization of PWA systems, based on linear and mixedinteger linear programming. As a result, given a set of initial conditions we are able to determine its partition into subsets of trajectories which are asymptotically stable, or unstable, or non-classifiable in T steps.