Implicit Linear Systems

1. Front Matter

   PDF

2. System models

   Pages 1-17

3. The Kronecker form

   Pages 19-23

4. Analysis of singularities

   Pages 25-35

5. Systems of minimal dimension

   Pages 37-66

6. Canonical representations

   Pages 67-81

7. Algebraic design applications

   Pages 83-118

8. Optimization with quadratic cost

   Pages 119-129

9. System identification

   Pages 131-142

10. Large-scale systems

    Pages 143-154

11. Extensions

    Pages 155-161

12. Back Matter

    PDF

These notes are an introduction to implicit models of linear dynamical systems, with applications to modelling, control system design, and identification, intended for control-system engineers at the beginning graduate level. Because they are non-oriented, the models are particularly useful where causality is unknown or may change. They are implicit in all variables and closed under the algebraic operations, and hence are useful for computer-aided analysis and design. They possess the vector-matrix conceptual simplicity and computational feasibility of state-space equations, together with the generality of matrix-fraction descriptions, and admit of canonical forms for which the joint identification of system parameters and dynamic variables is linear. The notes simplify, generalize, and complement much recent work on "singular" or "descriptor" models, but do not duplicate it. Sections are included on realizations, canonical forms, minimal representations, algebraic design applications, quadratic optimization, identification, large-scale systems, and extensions to multi-dimensional and time-varying systems.

• Algebra
• Identifikation
• Regelung
• Regelungssysteme
• calculus
• control
• control system
• dynamical systems
• dynamische Systeme
• modeling
• optimization
• system
• system identification

Policies and ethics