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Linear Dynamical Systems

In: Robust Control Systems

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  • Uwe Mackenroth

    (Fachhochschule Lübeck University of Applied Sciences, FB Maschinenbau und Wirtschaftsingenieurwesen)

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.

Suggested Citation

  • Uwe Mackenroth, 2004. "Linear Dynamical Systems," Springer Books, in: Robust Control Systems, chapter 0, pages 85-132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-09775-5_5
    DOI: 10.1007/978-3-662-09775-5_5
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