Getting Started

Interconnecting Linear Models

You can perform simple operations on LTI models, such as addition, multiplication, or concatenation. Addition performs a parallel interconnection. For example, typing

tf(1,[1 0]) + tf([1 1],[1 2])   % 1/s + (s+1)/(s+2)

produces this transfer function.

Transfer function
s^2 + 2 s + 2
-------------
  s^2 + 2 s

Multiplication performs a series interconnection. For example, typing

2 * tf(1,[1 0])*tf([1 1],[1 2])   % 2*1/s*(s+1)/(s+2)

produces this cascaded transfer function.

Transfer function:
2 s + 2
---------
s^2 + 2 s

If the operands are models of different types, the resulting model type is determined by precedence rules; see Precedence Rules under "Creating and Manipulating Models" online for more information. State-space models have highest precedence while transfer functions have lowest precedence. Hence the sum of a transfer function and a state-space model is always a state-space model.

Other available operations include system inversion, transposition, and pertransposition; see Arithmetic Operations online under "Creating and Manipulating Models." The Control System Toolbox also supports matrix-like indexing for extracting subsystems; see Extracting and Modifying Subsystems" online for more information.

You can also use the series and parallel functions as substitutes for multiplication and addition, respectively.

Table 2-2: Equivalent Ways to Interconnect Systems

Operator	Function	Resulting Transfer Function
sys1 + sys2	parallel(sys1,sys2)	Systems in parallel
sys1 * sys2	series(sys2,sys1)	Cascaded systems

Model Characteristics

Feedback Interconnection