Linear Dynamical Systems

Uwe Mackenroth
Additional contact information
Uwe Mackenroth: Fachhochschule Lübeck University of Applied Sciences, FB Maschinenbau und Wirtschaftsingenieurwesen

Chapter Chapter 5 in Robust Control Systems, 2004, pp 85-132 from Springer

Abstract: Abstract In this chapter, we consider state space representations of linear systems of ordinary differential equations with several inputs and outputs (MIMO systems). As in the SISO case, a linear system arises when a nonlinear system is linearized at an equilibrium state. All control theory methods developed in this book refer to linear systems and the nonlinearity of the original system has to be taken into account indirectly. After having introduced the linearization procedure, we give solution formulas for linear MIMO systems, characterize the stability and calculate the frequency response. Then, by deriving a state space representation for a general SISO transfer function, we are led in a natural way to four very important properties of linear systems, namely controllability, observability, stabilizability and detectability. Several characterizations of these properties are given and the Kaiman decomposition of the state space is presented. They are used in the formulation and the proofs of the theorems describing H 2 and H ∞ optimal controllers.

Keywords: Transfer Matrix; MIMO System; Linear Dynamical System; Lyapunov Equation; State Space Representation (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-09775-5_5

Ordering information: This item can be ordered from
http://www.springer.com/9783662097755

DOI: 10.1007/978-3-662-09775-5_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().