Hyperbolic Model-based Discrete Systems H_ ¡Þ Control

The dissertation mainly deals with the robust stabilization and the robust H_∞ control of uncertain nonlinear systems with Hyperbolic models. The main results can be listed as follows:In the first part, we focus on the problem of state feedback H_∞ control for a class of discrete-time uncertain systems with Hyperbolic models. The uncertainties are assumed to be of linear fractional form, which includes the norm-bounded uncertainty as a special case. By using Lyapunov function with PDD matrix, a sufficient LMI condition on robust stability with H_∞ norm bound is obtained. Moreover, a state feedback controller is developed to guarantee the closed-loop system being robustly stable. Finally, a numerical example is given to demonstrate the applicability of the proposed approach.In the second part, we study the problem of output feedback control for a class of discrete-time uncertain systems with Hyperbolic models. The uncertainties are assumed to be of norm-bounded form. By using Lyapunov function with PDD matrix and variable transformation, a sufficient condition on robust stability for this class of fuzzy systems is derived. Moreover, a robust control design approach is developed. Finally, a numerical example is given to demonstrate the application of the proposed approach.In the third part, we deal with the problem of output feedback H_∞ control for a class of discrete-time uncertain systems with Hyperbolic models. The uncertainties are assumed to be of linear fractional form, which can describe a class of rational nonlinearities. By using the property that negativeness of a matrix is not changed when its main diagonal blocks decrease, a nonlinear matrix inequality can be transformed into linear matrix inequalities(LMIS). Then a sufficient LMI condition on robust stability with H_∞ norm bound is obtained. Moreover, an output feedback controller can be constructed to guarantee the closed-loop system being robustly stable with H_∞ norm bound.