psys

Purpose

Specify polytopic or parameter-dependent linear systems

Syntax

• pols = psys(syslist) 
  affs = psys(pv,syslist) 
  

Description

psys specifies state-space models where the state-space matrices can be uncertain, time-varying, or parameter-dependent.

Two types of uncertain state-space models can be manipulated in the LMI Control Toolbox:

• Polytopic systems

E(t) = A(t)x + B(t)u

           y = C(t)x + D(t)u

• whose SYSTEM matrix takes values in a fixed polytope:

• 

• where S1, . . ., Sk are given "vertex" systems and

Co{S1, . . ., Sk} =

• denotes the convex hull of S1, . . ., Sk (polytope of matrices with vertices
  S1, . . ., Sk)

• Affine parameter-dependent systems

E(p) = A(p)x + B(p)u

       y = C(p)x + D(p)u

• where A(.); B(.), . . ., E(.) are fixed affine functions of some vector
  p = (p1, . . ., pn) of real parameters, i.e.,

• 

• where S0, S1, . . ., Sn are given SYSTEM matrices. The parameters pi can be time-varying or constant but uncertain.

Both types of models are specified with the function psys. The argument syslist lists the SYSTEM matrices Si characterizing the polytopic value set or parameter dependence. In addition, the description pv of the parameter vector (range of values and rate of variation) is required for affine parameter- dependent models (see pvec for details). Thus, a polytopic model with vertex systems S1, . . ., S4 is created by

• pols = psys([s1,s2,s3,s4])
  

while an affine parameter-dependent model with 4 real parameters is defined by

• affs = psys(pv,[s0,s1,s2,s3,s4])
  

The output is a structured matrix storing all the relevant information.

See Also

psinfo      Inquire about polytopic or parameter-dependent systems created with psys

pvec        Quantification of uncertainty on physical parameters

aff2pol     Convert affine parameter-dependent models to polytopic ones

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