The major topic of control problems is to modify the dynamics of a system such that some particular objects are satisfied. Control theory is benefited from practical activities and will be used to solve practical problems. Based on precise mathematical models, classic linear control theory tries to find a controller satisfying given performance index, while modern control theory aims to search the optimal controller such that the optimal performance index cab be realized. However, almost all of real systems may suffer uncertainties in different forms. The uncertainties include either model imperfections, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations, etc., or external disturbances, for examples, various disturbances with unknown statistical characteristic and bounded energy. For the analysis and synthesis of uncertain systems, this dissertation admits some tolerances of uncertainties, within which robust performances are guaranteed. Moreover, by optimization, the upper or lower bounds of performance index can be obtained instead of index itself.The work of this dissertation mainly addresses linear systems, which possess some kind of dynamics, such as time-delays, nonlinearity and stochastic jumps. The issues for robust controller synthesis cover many performances including stability, Hx, linear quadratic index, generalized H2, region pole location, etc.. Based on Lyapunov stability theory, quadratic stabilization theory for systems with time-varying but bounded uncertainties, linear matrix inequality and convex optimization approach, especially, introducing fuzzy and neural network models for nonlinear systems, a unified synthesis framework is formed under the state-space and is available for various practical control problem.In detail, the major contributions of this dissertation are as follows:1. Considering linear systems with time-varying but norm-boundeduncertainties, the Z,, index (peak-to-peak gain) robust controller is proposed by bounding the reachable set with inescapable ellipsoids.2. Extending generalized H2 control problems to a class of linear time-delay systems, the study results show that the controller synthesis problems can be cast to LMI (or BMI) feasibility problems in either memoryless state feedback case or dynamic output feedback case.3. The dissipative control problem is addressed for the uncertain linear discrete-time systems with delayed state perturbation, which covers norm-bounded, sector-bounded and positive real as its special cases. The uncertainties are also characterized by dissipativeness, which take into account more information and can reduce the conservation of analysis and synthesis.4. The stochastic positive real control problem is proposed for Markovian jump linear systems and then extended to the case with norm-bounded uncertainties. Under the state-space, the sufficient condition and synthesis methods of mode-dependent positive real controller are given in terms of LMI via both state-feedback and output-feedback.5. The robust D-stabilizable problem is discussed for a class of nonlinear uncertain systems. Applying Takagi-Sugeno fuzzy models and the notion of quadratic D-stability, for a given D-subrigion of the complex plane defined based on LMI representation, the robust D-stable condition is established in terms of the feasibility of a class of LMI's. The control synthesis is presented by using parallel distributed compensation technique.6. The problem of robust stability-based analysis and synthesis is discussed for a class of nonlinear dynamical systems modeled by multi-layer neural network. Furthermore, introducing linear quadratic index, an optimal guaranteed LQ index controller is presented for the nonlinear systems.7. For uncertain linear systems with both state and input delays, to guarantee its stability and avoid control inputs beyond given constraint levels, the constraint control problem... |