Feedback canonical forms of singular systems
نویسندگان
چکیده
Ex = Ax + Bu (1.1) where x e 3C ~ R" e % ~ R, (E, A, B)e R x R x R. Note that E and A are non square. We can always assume without loss of generality that B is monic. In the sequel, (1.1) will be referred to by the triple (E, A, B). Now, let I denote the set of all such (E, A, B)'s. Define T P D = {(W, V, G, FP, FD)eR qXq x R x x R x R x R with W, F a n d G non singular}. The action of this group on I is defined by:
منابع مشابه
Holomorphic canonical forms for holomorphic families of singular systems
In this paper we obtain a canonical reduced form for regularizable singular systems and we describe generic holomorphic families that permit us, to analyze the neighborhood of a given system. Key-Words:Singular systems, Feedback equivalence, Canonical form, Miniversal deformation.
متن کاملSingular Perturbation Theory in Output Feedback Control of Pure-Feedback Systems
This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer res...
متن کاملCanonical Forms of Singular 1d and 2d Linear Systems
The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical...
متن کاملDisturbance Decoupling for Singular Systems by Proportional and Derivative Feedback and Proportional and Derivative Output Injection
We study the disturbance decoupling problem for linear time invariant singular systems. We give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and derivative feedback and proportional and derivative output injection that also makes the resulting closed-loop system regular and/or of index at m...
متن کاملSensivity and stability of singular systems under proportional and derivative feedback
We consider triples of matrices (E,A, B), representing singular linear time invariant systems in the form Eẋ(t) = Ax(t) + Bu(t), with E, A ∈ Mp×n(C) and B ∈ Mn×m(C), under proportional and derivative feedback. Using geometrical techniques we obtain miniversal deformations that permit us to study sensivity and structural stability of singular systems. Key-Words:Singular linear systems, proportio...
متن کاملNormal Forms, Canonical Forms, and Invariants of Single Input Nonlinear Systems Under Feedback
We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analysing, step by step, the action of homogeneous transformations on the homogeneous part of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and show that two systems are equivale...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Kybernetika
دوره 27 شماره
صفحات -
تاریخ انتشار 1991