System stability in control system engineering

ISSTABLE True for stable filter FLAG = ISSTABLE(B,A) returns a logical output, FLAG, equal to TRUE if the filter specified by numerator coefficients B, and denominator coefficients A, is stable. Input vectors B, and A define a filter with transfer function: jw -jw -jmw jw B(e) b(1) + b(2)e + .... + b(m+1)e H(e) = ---- = ------------------------------------ jw -jw -jnw A(e) a(1) + a(2)e + .... + a(n+1)e FLAG = ISSTABLE(SOS) returns TRUE if the filter specified using the second order sections matrix, SOS, is stable. SOS is a Kx6 matrix, where the number of sections, K, must be greater than or equal to 2. Each row of SOS corresponds to the coefficients of a second order filter. From the transfer function displayed above, the ith row of the SOS matrix corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)]. FLAG = ISSTABLE(D) returns TRUE if the digital filter, D, is stable. You design a digital filter, D, by calling the designfilt function. % Example 1: % Create an unstable filter and verify its instability. b = [1 2 3 4 5 5 1 2]; % numerator coefficients a = [4 5 6 7 9 10 4 6]; % denominator coefficients flag = isstable(b,a) % determine if the filter is stable zplane(b,a) % zero-pole plot for filter % Example 2: % Create a filter and determine its stability for different % coefficient data types and tolerances. b = [1 -.5]; % numerator coefficients a = [1 -.999999999]; % denominator coefficients act_flag1 = isstable(b,a) % determine if its stable act_flag2 = isstable(single(b),single(a)) % becomes unstable due to % precision zplane(b,a) % zero-pole plot for filter % Example 3: % Design a Butterworth highpass IIR filter using second order sections % and determine its stability. [z,p,k] = butter(6,0.7,'high'); SOS = zp2sos(z,p,k); flag = isstable(SOS) % determine if the filter is stable zplane(z,p) % zero-pole plot for filter See also FILTERANALYZER, FILTORD, ISALLPASS, ISLINPHASE, ISMAXPHASE, ISMINPHASE Documentation for isstable doc isstable Other uses of isstable dsp.AllpassFilter/isstable DynamicSystem/isstable