Name
Abstract | ||
|---|---|---|
In this paper we propose a mechanisable technique for asymptotic stability analysis of continuous dynamical systems. We start from linearizing a continuous dynamical system, solving the Lyapunov matrix equation and then check whether the solution is positive definite. For the cases that the Jacobian matrix is not a Hurwitz matrix, we first derive an algebraizable sufficient condition for the existence of a Lyapunov function in quadratic form without linearization. Then, we apply a real root classification based method step by step to formulate this derived condition as a semi-algebraic set such that the semi-algebraic set only involves the coefficients of the pre-assumed quadratic form. Finally, we compute a sample point in the resulting semi-algebraic set for the coefficients resulting in a Lyapunov function. In this way, we avoid the use of generic quantifier elimination techniques for efficient computation. We prototypically implemented our algorithm based on DISCOVERER. The experimental results and comparisons demonstrate the feasibility and promise of our approach. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1145/1993886.1993933 | ISSAC |
Keywords | Field | DocType |
lyapunov matrix equation,jacobian matrix,hurwitz matrix,asymptotic stability analysis,lyapunov function,algebraic analysis,continuous dynamical system,method step,algebraizable sufficient condition,quadratic form,pre-assumed quadratic form,positive definite,quantifier elimination,dynamic system,lyapunov functions,matrix equation,asymptotic stability | Lyapunov function,Discrete mathematics,Lyapunov equation,Control-Lyapunov function,Mathematical analysis,Dynamical systems theory,Hurwitz matrix,Linearization,Lyapunov exponent,Mathematics,Stability theory | Conference |
Citations | PageRank | References |
6 | 0.84 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| zhikun she | 1 | 242 | 22.74 |
| Bai Xue | 2 | 46 | 6.55 |
| Zhiming Zheng | 3 | 128 | 16.80 |