Name
Abstract | ||
|---|---|---|
Recent research on switched and hybrid systems has resulted in a renewed interest in determining conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems. While efficient numerical solutions to this problem have existed for some time, compact analytical conditions for determining whether or not such a function exists for a finite number of systems have yet to be obtained. In this paper we present a geometric approach to this problem. By making a simplifying assumption we obtain a compact time-domain condition for the existence of such a function for a pair of LTI systems. We show a number of new and classical Lyapunov results can be obtained using our framework. In particular, we demonstrate that our results can be used to obtain compact time-domain versions of the SISO Kalman-Yacubovich-Popov lemma, the Circle Criterion, and stability multiplier criteria. Finally, we conclude by posing a number of open questions that arise as a result of our approach. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/978-3-540-30560-6_2 | European Summer School on Multi-AgentControl |
Keywords | Field | DocType |
lyapunov function,convex cone,compact time-domain condition,geometric approach,classical lyapunov result,stable lti system,compact time-domain version,finite number,circle criterion,linear system,common quadratic lyapunov function,lti system,compact analytical condition,time domain,mathematics statistics,hybrid system | Lyapunov function,Applied mathematics,Finite set,Circle criterion,Linear system,Control theory,Control-Lyapunov function,Lyapunov redesign,Hybrid system,Mathematics,Convex cone | Conference |
ISBN | Citations | PageRank |
3-540-24457-3 | 3 | 0.80 |
References | Authors | |
6 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robert Shorten | 1 | 3 | 0.80 |
| Oliver Mason | 2 | 71 | 5.67 |
| Kai Wulff | 3 | 340 | 21.94 |