DSSM – Discrete state space model of a linear system

Block SymbolLicensing group: ADVANCED

Function Description
The DSSM block (Discrete State Space Model) simulates behavior of a linear system

x(k + 1) = Adx(k) + Bdu(k),x(0) = x0 y(k) = Cdx(k) + Ddu(k),

where k is the simulation step, x(k) n is the state vector, x0 n is the initial value of the state vector, u(k) m is the input vector, y(k) p is the output vector. The matrix Ad n×n is the system dynamics matrix, Bd n×m is the input matrix, Cd p×n is the output matrix and Dd p×m is the direct transmission (feedthrough) matrix.

All matrices are specified in the same format as in Matlab, i.e. the whole matrix is placed in brackets, elements are entered by rows, elements of a row are separated by spaces (blanks), rows are separated by semicolons. The x0 vector is a column, therefore the elements are separated by semicolons (each element is in a separate row).

During the real-time simulation, single simulation step of the above discrete state space model is computed in each execution time instant.



Reset signal. When R1 = on, the state vector x is set to its initial value x0. The simulation continues on the falling edge of R1 (on off).



Simulation output holds its value if HLD=on.



Simulated system inputs. First m simulation inputs are used where m is the number of columns of the matrix Bd.  0.0

Double (F64)



Block error code


0 ....

O.K., the simulation runs correctly

-213 .

incompatibility of the state space model matrices dimensions

xxx ..

error code xxx of REXYGEN, see appendix C for details


Simulated system outputs. First p simulation outputs are used where p is the number of rows of the matrix Cd.

Double (F64)



Matrix Dd usage flag. If UD=offthen the Dd matrix is not used for simulation (simulation behaves as if the Dd matrix is zero).



Matrix (n × n) of the discrete linear system dynamics.

Double (F64)


Input matrix (n × m) of the discrete linear system.

Double (F64)


Output matrix (p × n) of the discrete linear system.

Double (F64)


Direct transmission (feedthrough) matrix (p × m) of the discrete linear system. The matrix is used only if the parameter UD=on. If UD=off, the dimensions of the Dd matrix are not checked.

Double (F64)


Initial value of the state vector (of dimension n) of the discrete linear system.

Double (F64)

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