An Overview of Emerging Trends in Nonlinear Control

Outline

• Linearization
• State Transition Matrix, Eigenvalues and Eigenvectors
• Controllability and Observability
• State Variable and Output Feedback, Pole-Placement Design, General Eigenstructure Assignment problem
• Full-Order Observers and Reduced-Order Observers
• An Introduction to the Calculus of Variations
• The Minimum Principle
• Linear-Quadratic Optimal Control. Optimal Regulators and Observers.
• References
  

State Transition Matrix:

An Autonomous Matrix Linear Differential Equation

Has A Solution of the Form:

The Matrix is Called The State Transition Matrix.

· Cayley-Hamilton Theorem:

Every Matrix Obeys Its Characteristic Equation

Useful in Improving the Accuracy and Efficiecy of Calculating Matrix Polynomials Such as:

Example: Computation of State Transition Matrices.

· Eigenvalues and Eigenvectors:

The Solution of an nxn Autonomous Matrix Differential Equation can be Expressed in the Form:

: Eigenvalues

: Eignvectors

: Mode Participation Constants

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