# Robustness and Worst-Case Analysis

Worst-case effect of uncertainty on stability, margins, and overshoot

A robust control system meets stability and performance requirements for all possible values of uncertain parameters. Although Monte-Carlo parameter sampling can yield a general idea of system performance across all uncertainty ranges, it cannot produce a guaranteed analysis of the worst-case parameter combination. The robustness analysis commands in this category directly calculate the upper and lower bounds on worst-case performance without random sampling. You can also calculate robustness margins that tell you how much variation in uncertain parameters the system can tolerate while maintaining stability or desired performance.

## Functions

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 `robstab` Robust stability of uncertain system `robgain` Robust performance of uncertain system `uscale` Scale uncertainty of block or system `robOptions` Option set for robustness analysis `gapmetric` Gap metric and Vinnicombe (nu-gap) metric for distance between two systems `lncf` Left normalized coprime factorization `rncf` Right normalized coprime factorization `ncfmargin` Calculate normalized coprime stability margin of plant-controller feedback loop `loopsens` Sensitivity functions of plant-controller feedback loop `sdhinfnorm` Compute L2 norm of continuous-time system in feedback with discrete-time system `sdlsim` Time response of sampled-data feedback system
 `wcgain` Worst-case gain of uncertain system `wcsigmaplot` Plot worst-case gain of uncertain system `wcnorm` Worst-case norm of uncertain matrix `wcOptions` Option set for worst-case analysis
 `mussv` Compute bounds on structured singular value (µ) `mussvextract` Extract `muinfo` structure returned by `mussv`

## Topics

### Robustness Analysis

Robustness and Worst-Case Analysis

Understand the relationships among measures of robust stability, robust performance, and worst-case gain.

Robust Stability and Worst-Case Gain of Uncertain System

Calculate the robust stability and examine the worst-case gain of a closed-loop uncertain system.

Worst-Case Sensitivity Functions of Feedback Loops

Use `wcgain` to compute the worst-case sensitivity and complementary sensitivity functions of feedback control structures.

Robust Stability, Robust Performance and Mu Analysis

Analyze and quantify the robustness of feedback control systems with uncertainty, and understand the relationship between robustness and the structured singular value, μ.

MIMO Robustness Analysis

Create a MIMO system with parametric uncertainty and analyze it for robust stability and worst-case performance.

Getting Reliable Estimates of Robustness Margins

Systems with only real uncertain parameters can have discontinuities in the structured singular value μ that hide robustness issues.

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