1. State Space Analysis and Controller Design
EEE3001 – EEE8013
State Space Analysis and Controller Design
This lecture will be recorded and
you will be able to download it
Dr Damian Giaouris
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2. Goals/Aims of Chapter 3 Basic form of a solution:
Distinct eigenvalues
Repeated eigenvalues
Complex eigenvalues
Eigenvalues/Eigenvectors
Particular soln given ICs
Response in the state space
Fundamental Solution Matrix

3. SOLUTION OF SS MODELS
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4. Eigenvalues & Solutions
a2=1 => a1=2
a1=2 => a2=-2
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5. Example C1 = 0.4 >> C=inv([2 1;1 -2])*[1;0]; C2 = 0.2
>> C1=C(1), C2=C(2)
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6. Example
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7. General Procedure
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8. 3 cases Distinct eigenvalues Repeated eigenvalues Complex eigenvalues
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9. Repeated Eigenvalues
Proceed as before
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10. Example
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11. Example
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12. Solution Matrices Fundamental Solution Matrix (FSM)
State Transition Matrix (STM)
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13. State Transition Matrix
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14. Exponential matrix
Exercise: Starting from the FSM prove that
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15. Exponential matrix
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