Tham khảo tài liệu 'adaptive control design and analysis part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 382 Chapter 9 Multivariable Adaptive Control The symbol Ỡ is used either in the partial derivative of ic with respect to X or in ỡ F s the degree of a polynomial matrix p s . A vector signal x t is bounded if a t L . Ik t c Vt 0 for some constant c 0 for both the CT case and DT case. The L1 signal norm of a vector signal x t is m - 111 Ể Jo 11 a t II dt in the CT case and Ik - 1 EiSo Ikơ ll in the DT case. An operator T D t of certain dimensions is linear if T D ữiUi a2 2 i 1T D - ui t a2T D - tỄ2 í for any constants Oil 2 and any vector signals Ui t Ii2 t . A linear operator T D t is stable and proper if for y t T D some constants p 0 a 0 and 7 0 all t 0 and any u t llỉ t ll llT -D - M i ll p i n r dr 7lk t ll Jq in the CT case or Ể-1 y i T r - u t 22e- ii 1-T u 7- 7 u t T 0 in the DT case where r t T D - u t denotes the convolution of the impulse response of T D with u - at t. A linear operator T D t is stable and strictly proper if it is stable with 7 0. A linear operator T D t has an impulse response matrix T t r in the sense that y t T D. . ii i ỉt0 T t r u r dr in the CT case or y ì T D - u t Eị t0 T t T u r in the DT case. For a linear time-invariant system its impulse response matrix is T f r T t r . In this section equations whose numbers have the letter C or D are used only for the CT or the DT case otherwise equations are used for both the CT and DT cases as a reminder CT stands for continuous time and DT stands for discrete time . Consider a rational transfer matrix ơo D e ỉMxAÍ D with a right coprime polynomial matrix decomposition GữỤD ZT D P 1 D . As in 171 442 the column degrees of Fr D pjj -D are dcj Pr D max Ỡ pý- D j 1 2 . M. Model Reference Adaptive Control 383 Introduce S c D diag D M1 D li2 and define rc Pr B Hm Pr D Sc P . Then Pr D is called column reduced 171 340 or column proper 282 if rc is nonsingular. Similar to that in Section for the case of rational functions a rational matrix Go -D is proper if .
