Decentralized variable structure control of uncertain linear large-scale systems (Q2747769)

One considers the large-scale system with uncertainty NEWLINE\[NEWLINE\dot x_i= (A_i+\Delta A_i) x_i+ B_i(I+\Delta B_i) u_i(t)+ \sum_{j\neq i} A_{ij} x_j+f_i,\quad i= 1,\dots, mNEWLINE\]NEWLINE with bounded uncertain elements. A sliding mode stabilizing feedback control is considered having the form NEWLINE\[NEWLINEu_i=- (G_iB_i)^{-1} G_i A_i x_i-{1\over 1-\delta_i} (G_i B_i)^{-1}[\alpha_i+ \beta_i|x_i|]\text{ sgn }S_i,NEWLINE\]NEWLINE where \(S_i= G_i x_i\) and \(\delta_i\) are those satisfying the inequality \(|\Delta B_i|\leq \delta_i< 1\).