Discontinuous Lyapunov functions for a class of piecewise affine systems
| Autor: | Farideh Cheraghi-Shami, Mohsen Mohammadian, Ali Akbar Gharaveisi, Malihe M. Farsangi |
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| Rok vydání: | 2018 |
| Předmět: |
Lyapunov function
0209 industrial biotechnology Pure mathematics Class (set theory) 020208 electrical & electronic engineering MathematicsofComputing_NUMERICALANALYSIS 02 engineering and technology symbols.namesake 020901 industrial engineering & automation Planar Exponential stability Partition refinement 0202 electrical engineering electronic engineering information engineering symbols State space Vector field Piecewise affine Instrumentation Mathematics |
| Zdroj: | Transactions of the Institute of Measurement and Control. 41:729-736 |
| ISSN: | 1477-0369 0142-3312 |
| DOI: | 10.1177/0142331218771138 |
| Popis: | In this paper, a Lyapunov-based method is provided to study the local asymptotic stability of planar piecewise affine systems with continuous vector fields. For such systems, the state space is supposed to be partitioned into several bounded convex polytopes. A piecewise affine function, not necessarily continuous on the boundaries of the polytopic partitions, is proposed as a candidate Lyapunov function. Then, sufficient conditions for the local asymptotic stability of the system, including a monotonicity condition at switching instants, are formulated as a linear programming problem. In addition, when the problem does not have a feasible solution based on the original partitions of the system, a new partition refinement algorithm is presented. In this way, more flexibility can be provided in searching for the Lyapunov function. Owing to relaxation of the continuity condition imposed on the system boundaries, the proposed method reaches to less conservative results, compared with the previous methods based on continuous piecewise affine Lyapunov functions. Simulation results illustrate the effectiveness of the proposed method. |
| Databáze: | OpenAIRE |
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