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# psys

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.

psys supports two types of uncertain state-space models:

• 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

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.

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

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