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Ajuda do Scilab >> Xcos > palettes > Matrix_pal > RICC

# RICC

Riccati Equation

### Description

This block computes the solution of Riccati equation using different method and for both case continuous and discrete.

When the Type parameter is set to:

• 1 : The Riccati equation in continuous time is: `A*X + X*A + C - X*D*X = 0`

• 2 : The Riccati equation in discrete time is: `A*X*(inv(In-D))*A - X + C = 0`

In this equations A is an NxN matrix, it is the first input of the block, C and D are two NxN symmetrics matrices and are respectively the second and third input of the RICC block. X represent the output of the block, it is also a NxN matrix.

The user can choose between two methods of computation with Model parameter. If this parameter is set to:

• 1 : the block uses the Schur method for the discret and continuous cases.

• 2 : the block uses the matrix sign function approach method for continuous time case and the inverse free spectral decomposition method for discret time case.

### Parameters

• Type (1=Cont 2=Disc)

For continuous time signal set this parameter to 1. For discrete input time set it to 2.

Properties : Type 'vec' of size 1.

• Model(1=Schr 2=sign(cont) inv(disc))

To use the Schur method in computation set this parameter to 1. To use matrix sign function approach in continuous case or the inverse free spectral decomposition method in discrete case set this parameter to 2.

Properties : Type 'vec' of size 1.

### Default properties

• always active: no

• direct-feedthrough: yes

• zero-crossing: no

• mode: no

• regular inputs:

- port 1 : size [-1,-1] / type 1

- port 2 : size [-1,-1] / type 1

- port 3 : 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: no

• discrete-time state: no

• object discrete-time state: no

• name of computational function: ricc_m

### Interfacing function

• SCI/modules/scicos_blocks/macros/MatrixOp/RICC.sci

### Computational function

• SCI/modules/scicos_blocks/src/c/ricc_m.c