Documentation

isstable

Determine whether system is stable

Syntax

B = isstable(sys)
B = isstable(sys,'elem')

Description

B = isstable(sys) returns a logical value of 1 (true) if the dynamic system model sys has stable dynamics, and a logical value of 0 (false) otherwise. If sys is a model array, then B = 1 only if all models in sys are stable.

B = isstable(sys,'elem') returns a logical array of the same dimensions as the model array sys. The logical array indicates which models in sys are stable.

isstable is only supported for analytical models with a finite number of poles.

Examples

collapse all

Create an array of SISO transfer function models with poles varying from -2 to 2. To do so, first initialize an array of dimension [1,length(a)] with zero-valued SISO transfer functions.

a = [-2:2];
sys = tf(zeros(1,1,1,length(a)));

Populate this array with transfer functions of the form 1/(s-a).

for j = 1:length(a)
sys(1,1,1,j) = tf(1,[1 -a(j)]);
end
sys.SamplingGrid = struct('a',a);

Examine the stability of the model array.

B_all = isstable(sys)
B_all = logical
0

By default, isstable returns a single Boolean value that is 1 (true) only if all models in the array are stable. sys contains some models with nonnegative poles, which are not stable. Therefore, isstable returns 0 (false) for the entire array.

Examine stability of each model in the array, element by element.

B_elem = isstable(sys,'elem')
B_elem = 1x5 logical array

1   1   0   0   0

The 'elem' flag causes isstable to return an array of Boolean values, which indicate the stability of the corresponding entry in the model array. For example, B_elem(2) = 1, which indicates that sys(1,1,1,2) is stable. This result is expected, because sys(1,1,1,2) has a = -1.