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Discrete-time systems and Z -transform

Discrete-time systems and Z -transform

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This chapter introduces the main theory and tools necessary to deal with computer-controlled systems, namely the L-transform, discrete-time models, controllability and observability conditions, and stability criteria. Most concepts presented for continuous-time systems can be adapted to the discrete-time case.

Chapter Contents:

  • 9.1 Fundamentals
  • 9.1.1 List of symbols
  • 9.1.2 Discrete-time systems preliminaries
  • 9.1.3 The Z-transform
  • 9.1.4 Discrete-time models
  • 9.1.4.1 Discretization of state-space models
  • 9.1.4.2 Discretization of transfer functions
  • 9.1.4.3 Poles and zeros of sampled transfer functions
  • 9.1.4.4 State-space representation of difference equations
  • 9.1.5 Controllability and observability
  • 9.1.6 Stability and the Routh-Hurwitz criterion
  • 9.2 Solved problems
  • 9.3 Proposed problems
  • 9.4 Discrete-time systems and Z-transform analysis using computer packages
  • 9.4.1 MATLAB
  • 9.4.2 SCILAB
  • 9.4.3 OCTAVE

Inspec keywords: discrete time systems; transforms; stability; continuous time systems; controllability; control system synthesis; observability

Other keywords: controllability condition; computer-controlled systems; L-transform; observability condition; stability criteria; discrete-time systems; continuous-time system; discrete-time model

Subjects: Stability in control theory; Control system analysis and synthesis methods; Integral transforms; Discrete control systems

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