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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.


isPassiveCheck passivity of linear systems
getPassiveIndexCompute passivity index of linear system
passiveplotCompute or plot passivity index as function of frequency
getSectorIndexCompute conic-sector index of linear system
getSectorCrossoverCrossover frequencies for sector bound
sectorplotCompute or plot sector index as function of frequency
sectorplotoptionsCreate list of relative index plot options



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.