Fast Algorithms for Computing Continuous Piecewise Affine Lyapunov Functions

2018 ◽  
pp. 274-299
Author(s):  
Sigurdur Hafstein
Keyword(s):  
Lyapunov Functions ◽  
Fast Algorithms ◽  
Piecewise Affine

Discontinuous Lyapunov functions for a class of piecewise affine systems

2018 ◽  
Vol 41 (3) ◽  
pp. 729-736 ◽  
Author(s):  
Farideh Cheraghi-Shami ◽  
Ali-Akbar Gharaveisi ◽  
Malihe M Farsangi ◽  
Mohsen Mohammadian
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Convex Polytopes ◽  
Sufficient Conditions ◽  
Monotonicity Condition ◽  
Piecewise Affine Systems ◽  
Affine Systems ◽  
Piecewise Affine ◽  
Local Asymptotic Stability

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.

scholarly journals Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse

2016 ◽  
Vol 49 (18) ◽  
pp. 13-18
Author(s):  
Tom R.V. Steentjes ◽  
Alina I. Doban ◽  
Mircea Lazar
Keyword(s):  
Finite Time ◽  
Lyapunov Functions ◽  
Piecewise Affine
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