Name
Abstract | ||
|---|---|---|
In this paper, we provide explicit solution formulae for higher order discrete 2D autonomous systems. We first consider a special type of 2D autonomous systems, namely, systems whose quotient modules are finitely generated as modules over the one variable Laurent polynomial ring ℝ[σ1±1].We then show that these solutions can be written in terms of various integer powers of a square 1-variable Laurent polynomial matrix A(σ1) acting on suitable 1D trajectories. We call this form of expressing the solutions a representation formula. Then, in order to extend this result to general 2D autonomous systems, we obtain an analogue of a classical algebraic result, called Noether's normalization lemma, for the Laurent polynomial ring in two variables. Using this result we show that every 2D autonomous system admits a representation formula through a suitable coordinate transformation in the domain ℤ2. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/CDC.2014.7039562 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
matrix algebra,polynomials,Noether normalization lemma,classical algebraic result,higher order discrete 2D autonomous systems,quotient modules,representation formulae,square 1-variable Laurent polynomial matrix,variable Laurent polynomial ring | Discrete mathematics,Finitely-generated abelian group,Mathematical analysis,Quotient module,Sigma,Laurent polynomial,Mathematics | Journal |
Volume | Issue | ISSN |
51 | 3 | 0743-1546 |
Citations | PageRank | References |
2 | 0.48 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Debasattam Pal | 1 | 28 | 12.84 |
| Harish K. Pillai | 2 | 90 | 20.79 |