Stabilization of an uncertain multiple-oscillator system

For a multiple-oscillator system that is subject to the uncertain gains ranging within compact sets,this paper presents a constructive stabilization design.Motivated by nested-saturation control methods,a nested controller that contains multiplicative coefficients is directly designed,and these coefficients are then determined in the stability analysis.By skillfully making transformations,elaborately constructing Lyapunov functions,and using an M-matrix principle,the stability analysis leads to the explicit inequality condition that is expressed by directly using the system parameters.