Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty
(Benchmark Results)


Example A

Test Case Plant Controller Sample Time
1 .b = { 0.548693198268086, -0.886738807003861 },
.a = { 1.0, -3.32481248817168, 1.64872127070013 }
.b = { -18.7913011069951, 11.3839445828215 },
.a = { 1.0, 3.63545078000333 }
0.5
2 .b = { 0.100342181002722, -0.110876810062963 },
.a = { 1.0, -2.12624017619613, 1.10517091807565 }
.b = { 18.5304651429392, -16.7960874196180 },
.a = { 1.0, -2.08535650257322 }
0.1
3 .b = { 0.0500422033454653, -0.0526068264456340 },
.a = { 1.0, -2.05640034257636, 1.05127109637602 }
.b = { 14.2344952240432, -13.5523885821810 },
.a = { 1.0, -1.42685562045612 }
0.05
4 .b = { 0.0300090687252212, -0.0309228417953966 },
.a = { 1.0, -2.03228208009387, 1.03045453395352 }
.b = { 12.9891735487942, -12.6121006969068 },
.a = { 1.0, -1.23596847805225 }
0.03
5 .b = { 0.0100003341716806, -0.0101008375175585 },
.a = { 1.0, -2.01025117377592, 1.01005016708417 }
.b = { 11.9254708617320, -11.8089453595694 },
.a = { 1.0, -1.07292051194339 }
0.01
6 .b = { 0.00500004171890647, -0.00502510442763112 },
.a = { 1.0, -2.00506264627685, 1.00501252085940 }
.b = { 11.6833505110710, -11.6261308811661 },
.a = { 1.0, -1.03580748101003 }
0.005
7 .b = { 0.00100000033341672, -0.00100100083375018 },
.a = { 1.0, -2.00100250116738, 1.00100050016671 }
.b = { 11.4958082843740, -11.4845259551093 },
.a = { 1.0, -1.00706037056799 }
0.001
8 .b = { 1.00000000003333e-05, -1.00001000008333e-05 },
.a = { 1.0, -2.00000100000250, 1.00000100000050 }
.b = { 11.4502063947756, -11.4500939644139 },
.a = { 1.0, -1.00007035781332 }
0.00001
9 .b = { 1.00000000000033e-06, -1.00000100000083e-06 },
.a = { 1.0, -2.00001000025000, 1.00001000005000 }
.b = { 11.4502063947756, -11.4500939644139 },
.a = { 1.0, -1.00007035781332 }
0.000001

Sample Time FWL Format
4-bits 8-bits 12-bits
0.5 fail fail fail
0.1 success success success
0.05 success success success
0.03 success success success
0.01 fail success success
0.005 fail success success
0.001 fail fail success
0.00001 fail fail fail
0.000001 fail fail fail

Example B

Test Case Plant Controller Sample Time
1 .b = { 0.335275509257994, -0.558786095915934 },
.a = { 1.0, -1.89055607640038, 0.778800783071405 }
.b = { -2.70561932258292, 4.91891416097458, -2.98975424265897, 0.607457221322442 },
.a = { 1.0, -0.246954439828182, -0.800014083515246, 0.356805858742342 }
0.5
2 .b = { 0.0927027117013712, -0.102460891523910 },
.a = { 1.0, -1.95610851441198, 0.951229424500714 }
.b = { -10.6541798765226, 28.9820624061405, -26.2822459536125, 7.94546415262250 },
.a = { 1.0, -0.976750653540241, -0.695199955503643, 0.688265939892838 }
0.1
3 .b = { 0.0481506869827621, -0.0506199529763825 },
.a = { 1.0, -1.97654454502514, 0.975309912028333 }
.b = { -19.2414736482723, 54.9701308152594, -52.3486145801513, 16.6178011176798 },
.a = { 1.0, -1.20633950872401, -0.423011266643906, 0.633303983755908 }
0.05
4 .b = { 0.0293305788581764, -0.0302238959805054 },
.a = { 1.0, -1.98555859816423, 0.985111939603063 }
.b = { -28.8602335012427, 84.0786290054145, -81.6496235908929, 26.4305091092668 },
.a = { 1.0, -1.39914676903959, -0.111714450559205, 0.512179344931653 }
0.03
5 .b = { 0.00992520776150855, -0.0100249585932822 },
.a = { 1.0, -1.99506235460857, 0.995012479192682 }
.b = { -58.8544737007610, 174.846413073101, -173.146281000398, 57.1542857242685 },
.a = { 1.0, -1.92141324780054, 0.863510897744980, 0.0580048403364478 }
0.01
6 .b = { 0.00498127600589352, -0.00500624480792807 },
.a = { 1.0, -1.99751560679848, 0.997503122397460 }
.b = { -79.8561004850143, 238.400671160303, -237.238792985947, 78.6942127596070 },
.a = { 1.0, -2.26995707001617, 1.54695565228205, -0.276981072005969 }
0.005
7 .b = { 0.000999250208276053, -0.00100024995835937 },
.a = { 1.0, -1.99950062485421, 0.999500124979169 }
.b = { -111.957457802305, 335.544346474481, -335.216643366135, 111.629754586207 },
.a = { 1.0, -2.79568196431083, 2.59175994708314, -0.796077785225516 }
0.001
8 .b = { 0.000399880013331867, -0.000400039997334000 },
.a = { 1.0, -1.99980009999067, 0.999800019998667 }
.b = { -119.158714850888, 357.336454078930, -357.196818781631, 119.019079546242 },
.a = { 1.0, -2.91304070183424, 2.82614887122274, -0.913108155920450 }
0.0004

Sample Time FWL Format
4-bits 8-bits 12-bits
0.5 fail success success
0.1 fail fail success
0.05 fail fail success
0.03 fail fail fail
0.01 fail fail fail
0.005 fail fail fail
0.001 fail fail fail
0.0004 fail fail fail