Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty
The large-scale interconnected system is \(\dot{x}_i=A_ix_i+f(x_i)+B_i[u_i+\Delta\Psi_i(x_i)]+ \sum_{j\neq i} H_{ij}(x_j)+\Delta H_i(x)\), \(y_i=C_i x_i\), \(i=1,\ldots,N\). The nonlinear functions \(f_i\) are continuous, \(\Delta\Psi_i(x_i)\) is the matched uncertainty, \(\sum_{j\neq i} H_{ij}(x_j)\) is the known interconnection, and \(\Delta H_i(x)\) includes all mismatched uncertainties. Under certain technical assumptions, among which some ``similarity'' of the subsystems \((A_i,B_i,C_i)\) is the most important one, a constructive proof is given of a sufficient condition for the existence of a continuous reduced-order controller stabilizing the system. Estimates for the stability regions are included. No structural information on uncertainties in subsystems or interconnections is required, except that they can be bounded by known functions of states and inputs. Good robustness is obtained because known and uncertain interconnections are treated separately.
scientific article; zbMATH DE number 1868225
scientific article