# Passivity and Sector Bounds

Analyze systems for passivity and arbitrary conic-sector bounds

Passive control is often part of the safety requirements in applications such as process control, tele-operation, human-machine interfaces, and system networks. Passivity is a particular case of the more general notion of sector bounds, the applications of which include absolute stability of feedback systems with static nonlinearities. Control System Toolbox™ includes tools for analyzing dynamic systems for both passivity and arbitrary sector bounds.

## Functions

 `isPassive` Check passivity of linear systems `getPassiveIndex` Compute passivity index of linear system `passiveplot` Compute or plot passivity index as function of frequency `getSectorIndex` Compute conic-sector index of linear system `getSectorCrossover` Crossover frequencies for sector bound `sectorplot` Compute or plot sector index as function of frequency `sectorplotoptions` Create list of relative index plot options

## Topics

### Passivity

A system is passive if it cannot produce energy on its own, and can only dissipate the energy that is stored in it initially. Passive control has applications such as process control, tele-operation, and human-machine interfaces.

Passivity Indices

Compute various measures of passivity for linear time-invariant systems.

Parallel Interconnection of Passive Systems

The parallel interconnection of passive systems is also passive.

Series Interconnection of Passive Systems

The series interconnection of passive systems is not necessarily passive.

Feedback Interconnection of Passive Systems

The feedback interconnection of passive systems is also passive.

### Sector Bounds

About Sector Bounds and Sector Indices

Sector bounds are constraints on the I/O trajectories of a system. Sector indices provide measures of how well a system’s trajectories fit into a particular sector.

Absolute Stability for Quantized System

This example shows how to enforce absolute stability when a linear time-invariant system is in feedback interconnection with a static nonlinearity that belongs to a conic sector.