Howtosignalprocessing
- How do you find the H-infinity norm of a transfer function?
- What is the H-infinity norm?
- What is infinity norm of a transfer function?
- How do you calculate H2 norm?
How do you find the H-infinity norm of a transfer function?
We can compute the transfer function H(s) by using the formula for block matrix inverse, [sI−A0−CTCsI+AT]−1=[(sI−A)−10(sI+AT)−1CTC(sI−A)−1(sI+AT)−1]. Hence, H(s)=[0BT][(sI−A)−10(sI+AT)−1CTC(sI−A)−1(sI+AT)−1][B0]+I=BT(sI+AT)−1CTC(sI−A)−1B+I.
What is the H-infinity norm?
The phrase H∞ control comes from the name of the mathematical space over which the optimization takes place: H∞ is the Hardy space of matrix-valued functions that are analytic and bounded in the open right-half of the complex plane defined by Re(s) > 0; the H∞ norm is the maximum singular value of the function over ...
What is infinity norm of a transfer function?
The infinity norm is the peak gain of the frequency response, that is, where denotes the largest singular value of a matrix. The discrete-time counterpart is. Usage. norm(sys) or norm(sys,2) both return the norm of the TF, SS, or ZPK model sys .
How do you calculate H2 norm?
The H2 norm of a continuous-time system with transfer function H(s) is given by: ‖ H ‖ 2 = 1 2 π ∫ − ∞ ∞ Trace [ H ( j ω ) H H ( j ω ) ] d ω . For a discrete-time system with transfer function H(z), the H2 norm is given by: ‖ H ‖ 2 = 1 2 π ∫ − π π Trace [ H ( e j ω ) H H ( e j ω ) ] d ω .
