A lthough the control of linear time invariant single-input single-output systems has reached a high level of maturity, the control of time varying and multivariable systems still needs to be explored a lot. In this dissertation, we introduce several novel nonlinear and adaptive control schemes for certain classes of time varying and multivariable plants as well as presenting a case study on adaptive control of practical time varying and multivariable systems.

We first design a control scheme for linear time varying (LTV) systems with known parameters. The control scheme is based on integrator backstepping, certainty equivalence, and normalizing damping. In our design, we employ a new param etrization and filter structure that takes into account the plant parameter variations. The control scheme guarantees exponential convergence of the tracking error to zero if the plant parameters are exactly known. If the parameters are not precisely known bu t the time variations of the parameters associated with the system zeros are known, the appropriate choice of certain design parameters, without using any adaptive law, leads to closed loop stability and perfect regulation. This control scheme is modified and supplem ented with an update law to be applicable to LTV plants with unknown param eters. In the adaptive control design, the notion of structured param eter variations is used in order to include possible a priori inform ation about the plant param eter variations. With this formulation, only the unstructured plant parameters are estim ated and are required to be slowly time varying, and the structured plant parameters are allowed to have any finite speed of variation. The adaptive controller is shown to be robust with respect to the unknown but slow param eter variations in the global sense. We derive performance bounds which can be used to select certain design parameters for performance improvement. We later modify our adaptive design in order to make it applicable to LTV system s with modeling errors. In the modified scheme, constructing the control law based on regulation of the estim ated tracking error instead of the actual one and use of normalizing dam ping plays the key roles in reaching the stability and robustness results. The properties of the proposed control schemes are dem onstrated using simulation results.

Next, we design and analyze a nonlinear control scheme for a general multivariable system to overcome some of the traditional parameterization issues. The design is based on switching and the theory of control Lyapunov functions. The new scheme guarantees stability and convergence of the output to a residual set by output-feedback if the plant parameters are known and by state-feedback if the plant parameters are unknown. The size of the residual set depends on some of the design parameters and can be made arbitrarily small. The proposed scheme has the potential to be extended for output-feedback control of multivariable plants with unknown parameters.

Finally, we present a case study on real time adaptive semiconductor process control. In the case study, single-input single-output and multivariable model based adaptive controllers for the electron cyclotron resonance (ECR) CF₄/O₂ plasm a etching of plasm a enhanced chemical vapor deposited (PECVD) silicon nitride thin films are designed and tested in sim ulation studies and in the laboratory on the actual etching chamber.