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.


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diskmarginDisk-based stability margins of feedback loops
dmplotInterpret disk gain and phase margins
gapmetricGap metric and Vinnicombe (nu-gap) metric for distance between two systems
lncfLeft normalized coprime factorization
rncfRight normalized coprime factorization
ncfmarginCalculate normalized coprime stability margin of plant-controller feedback loop
loopsensSensitivity functions of plant-controller feedback loop
sdhinfnormCompute L2 norm of continuous-time system in feedback with discrete-time system
sdlsimTime response of sampled-data feedback system
robstabRobust stability of uncertain system
robgainRobust performance of uncertain system
robOptionsOption set for robustness analysis
wcdiskmarginWorst-case disk-based stability margins of uncertain feedback loops
wcgainWorst-case gain of uncertain system
wcsigmaPlot worst-case gain of uncertain system
wcnormWorst-case norm of uncertain matrix
wcOptionsOption set for worst-case analysis
mussvCompute bounds on structured singular value (µ)
mussvextractExtract muinfo structure returned by mussv


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.

Stability Margins

Stability Analysis Using Disk Margins

Disk margins provide a stronger guarantee of stability than classical gain and phase margins.

Stability Margins of a Simulink Model

Compute classical and disk-based gain and phase margins of a control loop modeled in Simulink®.

Featured Examples