Tham khảo tài liệu 'new approaches in automation and robotics part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Switching Control in the Presence of Constraints and Unmodeled Dynamics 233 AtPj PjA PiBR-1BTPi -2aPi -Q 20 Using relation 20 the first term in 19 becames xT a BD ro T Pi Pi a BD ro x xT atPj Pja x xTDT ro BTPix xTPiD ro x xTPiBR-1BTPix - 2axTPix - xTQx xTDT ro BTPix xTPiBD ro x -xTPiBv - 2aV x - xTQx xTDT ro BT ro . Pix xTPiBD ro x vTPiv - 2aV x - xTQx - xTDT ro Riv - vTRiD ro x Also one can get xTQx xTDT ro Riv vTRiD ro x - avTRiv - avTRiv xTQx - 2xTDT ro BTPix - axKTRiKix avTRiv xT q -2Dt ro BTPi -aKTRiKi x avTRiv For a second and third terms in relation 19 we have satA - 1 k Kix T B BE ro T Pix xTPi B BE ro satA - 1 k Kix sat A - 1 k Ki T BTPix sat A - 1 k Ki T ET ro BTPix BxTPiBsat A - 1 k Kix xTPiB BE ro satA - 1 k Kix -satA - 1 k Kix T Riv - satA - 1 k Kix T ET ro Riv - - vTRisatA - 1 k Kix - vTRiE ro satA - 1 k Kix - sat a - 1 k Kix T et ro l Riv - vTRi et ro l sat a - 1 k Kix -2vTRi et ro l sat a - 1 k Kjx -2X min E ro l vTRisat a - 1 k M - 2 a. E ro l vTRisat A - 1 k M 23 From 19 and 21 - 23 and assumption A6 of Theorem follows V x 1 a vTRiv- 2aV x - xT q - 2DT ro BTPi -aKTRiKi x - - 2Xmm E ro l vTRisatA - 1 k kix -2aV x Xmin EH i vTRjv - xT . 21 22 234 New Approaches in Automation and Robotics q - 2Dt ro BTPi - aKTRiK x - 2Xmin E o l vTRtsatA - 1 k ktx - 2aV x - xT q - 2Dt m BtPj - aK1RiKi x .min E ro I - vj vj - 2satAj 1 k Ki vj Li 1. _ 24 In last relation is the vj is the j th element of vi -Kix . 1 . T_ . j v - b T P x -kix 25 j i j i i v ri From relation 17 one can get hl 1 p Aj 1 Pmax j Vx 6 Ci a Ei j 1 2 . m 26 and Pmax j is defined in the assumption of Theorem. For the x 0 we have two posibilites KI 2AjS is 6 S1 S1 j1 j2 L jp 27 and 2Ajs hl 1 Pmax jS Ajs js 6 S2 S2 jp 1 L jm 28 whereby 0 p m S1 S2 1 2 . m S1 n S2 ộ Using argument as in De Dona et al. 2002 one can get . T . . x 1 x ri 4 A 2 s p 1 í jỀ rij i lkiS k l p 1 J 29 From 24 and 29 follows . lx I in I I - J i ll X VW-2 vW u e i JÊr S vjs vjs -2satAls 1 k vjsP ri s 1 L iS -I s p
