Copositive Lyapunov functions for switched systems over cones. (English) Zbl 1159.93021
Summary: We answer two open questions on copositive Lyapunov functions which were recently posed by M. K. Çamlıbel and J. M. Schumacher [in: “Unsolved Problems in Mathematical Systems and Control Theory”, V. D. Blondel, A. Megretski (Eds.), Princeton University Press, 2004, pp. 189–193. Available online at http://press.princeton.edu/math/blondel/]. These questions are: what are necessary and sufficient conditions for the existence of a Lyapunov function for a linear system which is defined over a cone? How can the results be extended to switched linear systems where the system matrix varies over time?
We present conditions answering these questions. Our conditions amount to checking feasibility or infeasibility of a system of linear inequalities.
We present conditions answering these questions. Our conditions amount to checking feasibility or infeasibility of a system of linear inequalities.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C05 | Linear systems in control theory |
| 93D30 | Lyapunov and storage functions |
References:
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