| This dissertation focuses on linear systems with saturation nonlinearity and linear systems with delayed input. For linear systems with actuator saturation nonlinearity and disturbances, saturation nonlinearity is not required to be the standard saturation function and can be precisely or imprecisely known. Disturbances are either energy-bounded or magnitude-bounded. We first propose sufficient conditions for trajectory boundedness. On the basis of the obtained sufficient conditions, disturbance tolerance and rejection capabilities are defined and assessed. These capabilities can be improved by designing the linear state feedback gain. Furthermore, we address the anti-windup design problem for the same class of control systems. Different iterative algorithms are proposed to design the anti-windup compensation gain such that disturbance rejection and tolerance capabilities are improved. In the case that disturbances are input additive, we construct a parameterized state feedback law to practically globally stabilize a class of planar linear systems with actuator saturation. In addition, we initiate an IQC (Integral Quadratic Constraints) based approach to obtaining sufficient conditions under which an ellipsoid is contractively invariant for a single-input linear system under a saturated linear feedback law. It can be shown that the proposed conditions are necessary too.; For linear systems with delayed input, we start from considering an oscillator system. For any delay in the input, a state feedback law is proposed such that the closed-loop system is globally stabilized at the origin. Motivated by this result, the asymptotic stabilizability of linear systems with delayed input is examined. By explicit construction of stabilizing feedback laws, it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable. A simple example is constructed to show that such results would not be true if the open loop system is exponentially unstable. It is further shown that such systems, when subject to actuator saturation, are semi-globally asymptotically stabilizable by linear state or output feedback. |
