Inverse systems for reproducing linear functions of inputs

✍ Scribed by Tsuneo Yoshikawa; Toshiharu Sugie

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 458 KB
• Volume: 17
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(81)90024-8

✦ Synopsis

Most of the previous studies on inverse systems for some finite a. In other words, they regard systems which have treated only the case where all components of the input reproduce ath integral of the input of the original system as of the original system are recoverable. However, even when inverses. Hence the original input can be obtained by not all components are recoverable, there is still a possibility differentiating the output of the a-integral inverse ~, times. of reproducing part of the input. As a generalization of the Kamiyama and Furuta (1976) have proposed a further inverse of a linear time-invariant dynamical system to include generalized concept of 'minimal integral inverse'. They first such cases, 'a-integral F-inverse' is proposed in this paper define a [at,a 2 ..... ~]-integral inverse as a system satisfying which reproduces the ath integral of a linear function Fu of the input vector u. A necessary and sufficient condition for ~-~ 0S._. ~-0~ the existence of an a-integral F-inverse is derived. A construction procedure of such an inverse is also given along with a numerical example.