On the geometry of realizable Markov parameters by SIMO and MISO systems

详细信息    查看全文

• 作者：I. Baragañ ; a^a ; ¹ ; ^{itziar.baragana@ehu.es} ; F. Puerta^b ; ^{ferran.puerta@upc.edu} ; I. Zaballa^c ; ¹ ; ^{ion.zaballa@ehu.eus}
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：518
• 期：Complete
• 页码：97-143
• 全文大小：713 K
• 卷排序：518

文摘

Let p, m, n, d   be positive integers and let Ln(d)Ln(d) denote the set of sequences L=(L1,…,Ln)L=(L1,…,Ln) of p×mp×m real or complex matrices which are realizable by systems of minimal order d. It was shown in  and  that Ln(d)Ln(d) can be endowed with a structure of differentiable manifold when p=m=1p=m=1; that is, when the sequences are realizable by Single Input/Single Output (SISO) systems. In this paper a similar result is obtained for more general sequences. Specifically, we will consider the set Ln(r_,s_) of sequences L which are realizable by systems of minimal order d   and having r_ and s_ as Brunovsky indices of controllability and observability, respectively. It is shown in this paper that when one of the two collections of indices r_ or s_ is constant, then Ln(r_,s_) can be provided with a structure of differentiable manifold and a formula of its dimension is given. The special cases r_=(1,…,1) or s_=(1,…,1) correspond to sequences realizable, respectively, by Single Input/Multi Output (SIMO) or Multi Input/Single Output (MISO) systems.