~~~~~qf,rq;r 'I1'f 23 3l'if; 1 "B 2015 '1:. 48-53 11R ~ Till ~ ~ ~ illfR llfOm ~, ~ sfI~lfTlctl ~, qc;;rr 800013 (~) mmT : ~ ~im-1:f?rjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA if ~ ~ f.lwrc:n itl cf; flYljQIRtCfl ~ ~~ ctT ~ cf; ~ ;r:ft fcrfu ~ ctT 1"f1fi % I~ fcrfu ~ ~ ton "C1'ffi~-~ cf; ];l11Tq -en: ~ % I~ ~ cf; lTIUfI1 ~ ,W!; lfiT ~ f.lwrc:n itl CflT ~ ~ itl if ~ llm %, ~ TTfCfl ~ ~ fclWsG ~ CflT ~ ~ ~ I~ ~ ~ ton "C1'ffi~ CflT ~ ~ ~ zm W!; ~ f.lwrc:n itl cf; TTfCfl ~ cf; lTIUfI1 ~ ~ fctm llm % I ~~ cf; ~ cf; ~ ~ ~ COT ~ fctm llm % I ;JRf if ~ Fctfu ctT ~ CflT G~Tf.r cf; ~ ~ '1ft ~ fctm llm % I Proportional derivative observer design for rectangular linear descriptor systems Mahendra Kumar Gupta & Nutan Kumar Tomar Department of Mathematics, Indian Institute of Technology, Patna 800013 (Bihar) Abstract A new method is proposed to design a proportional derivative (PO) observer for rectangular linear time invariant descriptor systems. The method is based on the effects of full column rank matrix transformations. By these transformations, given descriptor systems has been transformed into a equivalent system satisfying certain conditions. These full column rank matrices are derived from the coefficient matrices of the given descriptor system using simple matrix theory. Sufficient conditions for the existence of observers are given and proved. An illustrative example is provided to demonstrate the effectiveness of the proposed method. !HfiI tFtI ~ ~ G:!?TCfiT if ~ !?~0if ~ ~ cf?r cfi f<T!?Wsrrr JfR ~ cnT ~ \3lfuq) ~ R<:rr ~, CRiffcfl ~ cf?r tT fctffi Cli(=(1 \?1Ch f.1cfiT<l Ch'T ~ ~ q)T ~ quf;r CR wo€t ~ 1-3 I fctffi m 011<1d IChi{ ~ "ffl11T f.l!?TR ~ cf?r cnT fTlyRlf@d ~ if ffi® \i1T Wfiill ~IQPONMLKJIHGFEDCBA EX = Ax+ ii«. (La) cbaZYXWVUTSRQPONMLKJIHGFEDCBA y = ex, (Ib) ~ x ERn, U E R\ Y E R", ~!?T: \3lCWlT OOT, \3lfllCi ~!?r JfR ~ ~!?T ~I~ E E R IIIX ", A E R lllxn , jj E R",Xk, JfR C E R.PXI/ ~ 0lTR ~!?T ~ ~'tli (E) = no <~ {m, n}, cf?r (1) cnT ~ ~ cf?r ~~, ~ m = n JfR :'JA, EC~ ~ <mfOlCh (A E- A) '" o. ~ ~ E JfR A ~ ~ JfR E '1&hliU~<1 tIT, ill cf?r (1) cnT SH1llil"ll cf?r ~ ~ I fTI<1'?lU~<1dl JfR ~ Ch'T ~ cnT.~ ci?lT~ 011<1dIChI{ ci?lT cfi ~ \?1(=(1IRd M lTm ~ 33 IW ~ cnT ~ m~ JfR fTlyRlRstd ~ (H 1) JfR (H2) q)T ~ CR ~ 011<1dIChI{ ~ ci?lT cfi ~ ~ ~ !?~cnT~ml (Hl)~ l~~ l ~n+~ (£), IAE -1J (H2) 'tli L C = n VA E (C+ ~ cwtt ~~ -msm0if q)T ~ ~ JfR (C+ = {SISEC, Re (s) ~O} ~ ~ ~~ ~ ~ I 1. cf?r (1) ~-g~ ChC;ij1ldl ~~~~ (HI) q)T 1:ffi'R" Cfi«fT tIT I