LTISystem

Purpose

Represents linear time-invariant systems

Syntax

sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'T_s', Ts)

Description

This class represents linear time-invariant systems of the form

../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem8.png

where ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem1.png is the state vector, ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem2.png is the vector of inputs, ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem3.png is the vector of outputs, and ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem4.png represents the sampling time.

Each LTI system defines following properties: To define an LTI system, provide the list of system's matrices to the constructor:

sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'Ts', Ts) All inputs, except of the A matrix, can be omitted. In such a case they are set to empty matrices of corresponding dimension. As a consequence, one can easily define autonomous systems ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem5.png by calling sys = LTISystem('A', A, 'f', f, 'Ts', Ts). Similarly, to define an LTI system without outputs, call sys = LTISystem('A', A, 'B', B, 'Ts', Ts). If the sampling time is omitted, it is set to Ts=1.

Another option to define an LTI system is to import the dynamics from Control toolbox' discre-time state-space objects:

sys = LTISystem(ss(A, B, C, D, Ts)) Important to remember is that LTI systems carry with them the value of the state vector. The initial value can be set by the sys.initialize(x0) method (see "help LTISystem/initialize"). Value of the internal state can be retrieved by the sys.getStates() method (see "help LTISystem/getStates"). To update the internal state using the system's state-update equation, use the sys.update(u) function (see "help LTISystem/update").

Example(s)

Example 1

Create a 1D LTI system ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem6.png, ../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem7.png
sys = LTISystem('A', 2, 'B', 1, 'C', 3)
LTISystem with 1 state, 1 input, 1 output

See Also

pwasystem


© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk