CDS 110b: State Estimation

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Course Home

L7-2: Sensitivity

L8-1: Robust Stability

L9-1: Robust Perf

Schedule

This lecture presents an introduction to state estimation and observers. Beginning with a definition of observability, we provide conditions under which a linear system is observable and show how to construct an observer in the case where there is no noise. We then prove the separation principle, which shows how to combine state regulation with state estimation.

Lecture Outline

1. Observability
   • Definition of observability (full nonlinear system)
   • Observability conditions for linear processes
     • Intuition: Derivation via differentiation
     • Formal proof
2. State Estimation
   • Intuition: offline estimation
   • Luenberger observer
   • Example
3. Separation Principle
   • Proof of the separation principle
   • Transfer function representation
   • Youla parameterization (if time)

Lecture Materials

• Lecture Presentation (MP3)
• Optional reading: AM05, Sections 6.x
• Homework 4