On the synthesis of linear control systems with specified characteristics

✍ Scribed by Juergen E. Ackermann

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 438 KB
• Volume: 13
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(77)90012-7

✦ Synopsis

The Popov invariants are used to define two matrices M^B and /(As, which describe the properties of a system ~ = Ax + Bu in a basis-independent form. Also a control system with state feedback K and nonsingular input transformation M, :~ = (A -BK)x + BMw = Fx + Gw, can be uniquely specified by the corresponding matrices M~ and Kn~, which may be chosen arbitrarily with the only condition, that (F, G) must have the same unordered set of Kronecker invariants as (A, B). It is shown, how K and M are computed from M~s, K^a, M~ and K~. Implications for pole assignment, minimal polynomial assignment and observer design are shown. Also a solution to the minimal realization problem is given, which results in MAB, /(As and the output relation y = Cx.