Removing the input derivatives in the generalized bilinear state equations

Proceedings of the Estonian Academy of Sciences

Tanel Mullari¹  Alan S. I. Zinober¹  Ãœlle Kotta¹  Maris Tõnso¹  Palle Kotta¹ 

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关键词: control systems;    bilinear systems;    differential input-output equations;    state-space realization;   

DOI  :  10.3176/proc.2009.2.02

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

The paper suggests constraints on the coefficients ai, bi, cij of the bilinear continuous-time input-output model that yield generalized state equations with input derivative order lower than that in the input-output equations. In the limiting case when one removes the input derivatives altogether, these conditions provide a solution of the realizability problem. The new state coordinates are found step by step. We first find a coordinate transformation allowing the reduction of the maximal order of the input time derivatives by one and write the corresponding state equations. At the second step we find the next coordinate transformation to lower the maximal order of input time derivative in the new state equations, etc. At each step we check, what condition the coefficients should satisfy to make the next step possible.

【 授权许可】

Unknown