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# CLSS

Continuous state-space system

### Block Screenshot

### Contents

### Palette

### Description

This block realizes a continuous-time linear state-space system.

where **x** is the vector of state
variables, **u** is the vector of input
functions and **y** is the vector of output
variables.

The system is defined by the **(A, B, C, D)** matrices and the initial state **X0**.
The dimensions must be compatible.

### Dialog box

**A matrix**A square matrix.

Properties : Type 'mat' of size [-1,-1].

**B matrix**The

**B**matrix, [] if system has no input.Properties : Type 'mat' of size ["size(%1,2)","-1"].

**C matrix**The

**C**matrix , [] if system has no output.Properties : Type 'mat' of size ["-1","size(%1,2)"].

**D matrix**The

**D**matrix, [] if system has no D term.Properties : Type 'mat' of size [-1,-1].

**Initial state**A vector/scalar initial state of the system.

Properties : Type 'vec' of size "size(%1,2)".

### Default properties

**always active:**yes**direct-feedthrough:**no**zero-crossing:**no**mode:**no**regular inputs:****- port 1 : size [1,1] / type 1****regular outputs:****- port 1 : size [1,1] / type 1****number/sizes of activation inputs:**0**number/sizes of activation outputs:**0**continuous-time state:**yes**discrete-time state:**no**object discrete-time state:**no**name of computational function:***csslti4*

### CLSS Example

This sample example illustrates how to use CLSS block to simulate
and display the output waveform **y(t)=Vc(t)** of the RLC circuit shown below.

The equations for an RLC circuit are the following. They result from Kirchhoff's voltage law and Newton's law.

The R, L and C are the system's resistance, inductance and capacitor.

We define the capacitor voltage `Vc`

and the
inductance current `iL`

as the state variables
`X1`

and `X2.`

thus

Rearranging these equations we get:

These equations can be put into matrix form as follows,

The required output equation is

The following diagram shows these equations modeled in Xcos where R=10Ω, L=5 mΗ and C=0.1µF; the initial states are x1=0 and x2=0.5.

To obtain the output Vc(t) we use CLSS block from Continuous time systems Palette.

### Interfacing function

SCI/modules/scicos_blocks/macros/Linear/CLSS.sci

### Computational function

SCI/modules/scicos_blocks/src/c/csslti4.c (Type 4)

### Authors

**Zhour Madini-Zouine**DIGITEO

## Comments

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