Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
The stability of saturated linear dynamical systems is undecidable
Journal of Computer and System Sciences
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Decompositional Construction of Lyapunov Functions for Hybrid Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Condition number based complexity estimate for computing local extrema
Journal of Computational and Applied Mathematics
Condition number based complexity estimate for solving polynomial systems
Journal of Computational and Applied Mathematics
SIAM Journal on Control and Optimization
Algebraic analysis on asymptotic stability of continuous dynamical systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing a basin of attraction to a target region by solving bilinear semi-definite problems
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Model checking of hybrid systems: from reachability towards stability
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Verifiable conditions on asymptotic stabilisability for a class of planar switched linear systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
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In this paper we propose a mechanisable approach for discovering multiple Lyapunov functions for switched hybrid systems. We start with the classical definition on asymptotic stability, which can be assured by the existence of multiple Lyapunov functions. Then, we derive an algebraizable sufficient condition on multiple Lyapunov functions in quadratic form for asymptotic stability analysis. Since different modes are considered, in addition to real root classification, we further apply a projection operator step by step to under-approximate this sufficient condition and obtain a set of semi-algebraic sets which only involve the coefficients of the multiple Lyapunov function. Moreover, for each step, we use the information on modes to optimize our intermediate computation results. Finally, we compute a sample point in the resulting semi-algebraic sets for coefficients. We tested our approach on five examples using prototypical implementation. The computation and comparison results demonstrate the applicability and efficiency of our approach.