popov :: Functions (Robust Control Toolbox™)

Contents

Index

• Getting Started

• Uncertain Elements

• Uncertain Matrices and Systems

• Manipulation of Uncertain Models

• Interconnection of Uncertain Models

• Model Order Reduction

• Robustness and Worst-Case Analysis

• Robustness Analysis for Parameter-Dependent Systems (P-Systems)

• Controller Synthesis

• µ-Synthesis

• Sampled-Data Systems

• Gain Scheduling

• Frequency-Response Data (FRD) Models

• Supporting Utilities

• LMIs

• Modification of Systems of LMIs

• Release Notes

popov

Purpose

Perform Popov robust stability test

Syntax

```
[t,P,S,N] = popov(sys,delta,flag) 
```

Description

popov uses the Popov criterion to test the robust stability of dynamical systems with possibly nonlinear and/or time-varying uncertainty. The uncertain system must be described as the interconnection of a nominal LTI system sys and some uncertainty delta.

The command

```
[t,P,S,N] = popov(sys,delta)
```

tests the robust stability of this interconnection. Robust stability is guaranteed if t < 0. Then P determines the quadratic part x^TPx of the Lyapunov function and D and S are the Popov multipliers.

If the uncertainty delta contains real parameter blocks, the conservatism of the Popov criterion can be reduced by first performing a simple loop transformation. To use this refined test, call popov with the syntax

```
[t,P,S,N] = popov(sys,delta,1) 
```

See Also

quadstab Quadratic stability of polytopic or affine parameter-dependent systems

pdlstab Robust stability of polytopic or affine parameter-dependent systems (P-system)

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