What is $H_2$ and $H_{\infty}$ control? [closed]

1. What is H2 and H-infinity control?
2. What is H2 controller?
3. What is H2 norm?
4. How does H-infinity control work?

What is H2 and H-infinity control?

H2 and H-infinity contool theories involve suppressing the sensitivity matrix transfer. function at the lower frequencies for high gain performance and suppressing the trans- missivity at higher frequencies, i.e. loop shaping.

What is H2 controller?

H2 -optimization finds a controller which minimizes the H2. norm of the closed-loop transfer function and internally stabilizes the system. The polynomial solution of. the standard H2 problem is proposed in Meinsma (2000), which is based on factorizations over. polynomials and stable matrices.

What is H2 norm?

H2 norm. The H₂ norm of a stable system H is the root-mean-square of the impulse response of the system. The H₂ norm measures the steady-state covariance (or power) of the output response y = Hw to unit white noise inputs w: ‖ H ‖ 2 2 = lim E t → ∞ y ( t ) T y ( t ) , E ( w ( t ) w ( τ ) T ) = δ ( t − τ ) I .

How does H-infinity control work?

H_∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H_∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization.