REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
NP-Hardness of Some Linear Control Design Problems
SIAM Journal on Control and Optimization
The stability of saturated linear dynamical systems is undecidable
Journal of Computer and System Sciences
Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
The ConstructibleSetTools and ParametricSystemTools Modules of the RegularChains Library in Maple
ICCSA '08 Proceedings of the 2008 International Conference on Computational Sciences and Its Applications
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
Algebraic analysis on asymptotic stability of switched hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Stability results for switched controller systems
Automatica (Journal of IFAC)
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In this paper, we propose a computer algebra based approach for analyzing asymptotic stabilisability of a class of planar switched linear systems, where subsystems are assumed to be alternatively active. We start with an algebraizable sufficient condition on the existence of stabilizing switching lines and a multiple Lyapunov function. Then, we apply a real root classification based method to under-approximate this condition such that the under-approximation only involves the parametric coefficients. Afterward, we additionally use quantifier elimination to eliminate parameters in the multiple Lyapunov function, arriving at a quantifier-free formula over parameters in the switching lines. According to our intermediate under-approximation as well as our final quantifier-free formula, we can easily design explicit stabilizing switching laws. Moreover, based on a prototypical implementation, we use an illustrating example to show the applicability of our approach. Finally, the advantages of our approach are demonstrated by the comparisons with some related works in the literature.