* * * LINEAR SYSTEMS TOOLKIT * Version 0.99 * Released in August 2004 * * * * Decompositions of Autonomous Systems ssd - continuous-time stability structural decomposition . . 1 dssd - discrete-time stability structural decomposition . . . 2 jcf - Jordan canonical form . . . . . . . . . . . . . . . . 3 rjd - real Jordan decomposition . . . . . . . . . . . . . . 4 * Decompositions of Unforced and Unsensed Systems osd - observability structural decomposition . . . . . . . . 5 obvidx - observability index . . . . . . . . . . . . . . . . . 6 bdosd - block diagonal observable structural decomposition . . 7 csd - controllability structural decomposition . . . . . . . 8 ctridx - controllability index . . . . . . . . . . . . . . . . 9 bdcsd - block diagonal controllable structural decomposition . 10 * Decompositions and Structural Properties of Proper Systems scbraw - raw decomposition without integration chains . . . . . 11 scb - structural decomposition of continuous-time system . . 12 dscb - structural decomposition of discrete-time system . . . 13 kcf - Kronecker canonical form of a system matrix . . . . . 14 morseidx - Morse indices . . . . . . . . . . . . . . . . . . . . 15 blkz - blocking zeros . . . . . . . . . . . . . . . . . . . . 16 invz - invariant zero structure . . . . . . . . . . . . . . . 17 infz - infinite zero structure . . . . . . . . . . . . . . . 18 l_invt - left invertibility structure . . . . . . . . . . . . . 19 r_invt - right invertibility structure . . . . . . . . . . . . 20 normrank - normal rank . . . . . . . . . . . . . . . . . . . . . 21 v_star - weakly unobservable subspace . . . . . . . . . . . . . 22 v_minus - stable weakly unobservable subspace . . . . . . . . . 23 v_plus - unstable weakly unobservable subspace . . . . . . . . 24 s_star - strongly controllable subspace . . . . . . . . . . . . 25 s_minus - stable strongly controllable subspace . . . . . . . . 26 s_plus - unstable strongly controllable subspace . . . . . . . 27 r_star - controllable weakly unobservable subspace . . . . . . 28 n_star - distributionally weakly unobservable subspace . . . . 29 s_lambda - geometric subspace S_{lambda} . . . . . . . . . . . . 30 v_lambda - geometric subspace V_{lambda} . . . . . . . . . . . . 31 * Operations of Vector Subspaces ssorder - ordering of vector subspaces . . . . . . . . . . . . . 32 ssintsec - intersection of vector subspaces . . . . . . . . . . . 33 ssadd - addition of vector subspaces . . . . . . . . . . . . . 34 * Decompositions and Properties of Descriptor Systems ea_ds - decomposition of a matrix pair (E,A) . . . . . . . . . 35 sd_ds - decomposition for descriptor systems . . . . . . . . . 36 invz_ds - descriptor system invariant zero structure . . . . . . 37 infz_ds - descriptor system infinite zero structure . . . . . . 38 l_invt_ds - descriptor system left invertibility structure . . . . 39 r_invt_ds - descriptor system right invertibility structure . . . 40 * System Factorizations mpfact - continuous-time minimum-phase/all-pass factorization . 41 iofact - continuous-time inner-outer factorization . . . . . . 42 gcfact - continuous-time generalized cascade factorization . . 43 dmpfact - discrete-time minimum-phase/all-pass factorization . . 44 diofact - discrete-time inner-outer factorization . . . . . . . 45 * Structural Assignment via Sensor/Actuator Selection sa_sen - structural assignment via sensor selection . . . . . . 46 sa_act - structural assignment via actuator selection . . . . . 47 * Asymptotic Time-scale and Eigenstructure Assignment (ATEA) atea - continuous-time ATEA . . . . . . . . . . . . . . . . . 48 gm2star - infimum for continuous-time H2 control . . . . . . . . 49 h2care - solution to continuous-time H2 ARE . . . . . . . . . . 50 h2state - solution to continuous-time H2 control . . . . . . . . 51 gm8star - infimum for continuous-time H-infinity control . . . . 52 h8care - solution to continuous-time H-infinity ARE . . . . . . 53 h8state - solution to continuous-time H-infinity control . . . . 54 addps - solution to continuous-time disturbance decoupling . . 55 datea - discrete-time ATEA . . . . . . . . . . . . . . . . . . 56 dare - solution to general discrete-time ARE . . . . . . . . 57 dgm2star - infimum for discrete-time H2 control . . . . . . . . . 58 h2dare - solution to discrete-time H2 ARE . . . . . . . . . . . 59 dh2state - solution to discrete-time H2 control . . . . . . . . . 60 dgm8star - infimum for discrete-time H-infinity control . . . . . 61 h8dare - solution to discrete-time H-infinity ARE . . . . . . . 62 dh8state - solution to discrete-time H-infinity control . . . . . 63 daddps - solution to discrete-time disturbance decoupling . . . 64 * Disturbance Decoupling Problem with Static Output Feedback (DDPCM) ddpcm - solution to DDPCM . . . . . . . . . . . . . . . . . . 65 rosys4ddp - irreducible reduced-order system that can be used to solve DDPCM . . . . . . . . . . . . . . . . . . . . 66 * * E N D * O F * L I N E A R * S Y S T E M S * T O O L K I T * *