Necessary and sufficient condition in Lyapunov robust control: Multi-input case

Autor:	C. H. Chao, H. L. Stalford
Rok vydání:	1990
Předmět:	Lyapunov function Discrete mathematics Control and Optimization Applied Mathematics Linear system Block (permutation group theory) Order (ring theory) Management Science and Operations Research symbols.namesake Kronecker delta symbols Canonical form Robust control Matrix calculus Mathematics
Zdroj:	Journal of Optimization Theory and Applications. 66:1-21
ISSN:	1573-2878 0022-3239
DOI:	10.1007/bf00940529
Popis:	We consider a linear time-invariant finite-dimensional system x=Ax+Bu with multi-inputu, in which the matricesA andB are in canonical controller form. We assume that the system is controllable andB has rankm. We study the Lyapunov equationPA+A T P+Q=0, withQ>0, and investigate the properties thatP must satisfy in order that the canonical controller matrixA be Hurwitz. We show that, for the matrixA being Hurwitz, it is necessary and sufficient thatB T PB>0 and that the determinant ofB T PW be Hurwitz, whereW=block diag[w 1,...,w m ], with elementw i =[s k i −1,s k i −2,...,s, 1] T ; here, the symbolsk i ,i=1, 2, ...,m, denote the Kronecker invariants with respect to the pair {A, B}. This result has application in designing robust controllers for linear uncertain systems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7c2cb92e2b6013f987144586bc029ef6 https://doi.org/10.1007/bf00940529 Zobrazit plný text záznamu Full text from SpringerLink