A two-time-scale linear system with uncertain time-varying parameter is to be stabilized. A class of robust composite controls is proposed. The control renders the system practically stable regardless of the true value of the parameter. The control scheme consists of linear and nonlinear parts. The linear part is designed via a two-level optimization setting. No matching condition is needed for the linear control. The nonlinear part is of continuous saturation type. Matching condition is needed for the nonlinear control. However, it can be achieved by choosing the boundary layer model appropriately.
Robust Composite Control for Singularly Perturbed Systems With Time-Varying Uncertainties
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Chen, Y. H., and Chen, J. S. (December 1, 1995). "Robust Composite Control for Singularly Perturbed Systems With Time-Varying Uncertainties." ASME. J. Dyn. Sys., Meas., Control. December 1995; 117(4): 445–452. https://doi.org/10.1115/1.2801099
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