This thesis investigates a robust control problem of discrete-time systems, and proposes a polynomial approach to design the optimal controller that achieves the best robust performance.

Over the past few decades, robust control theory has gained major attention within the entire systems and control community, for its significant impact on various engineering areas such as aerospace control and process control. A fundamental issue in robust control is to characterize model uncertainties. A good uncertainty model should capture a substantial class of perturbations of the nominal plant and be mathematically tractable. While the additive and multiplicative uncertainty models are well-studied and commonly used, they may show some incapableness in fully characterizing model uncertainties fo...[ Read more ]

This thesis investigates a robust control problem of discrete-time systems, and proposes a polynomial approach to design the optimal controller that achieves the best robust performance.

Over the past few decades, robust control theory has gained major attention within the entire systems and control community, for its significant impact on various engineering areas such as aerospace control and process control. A fundamental issue in robust control is to characterize model uncertainties. A good uncertainty model should capture a substantial class of perturbations of the nominal plant and be mathematically tractable. While the additive and multiplicative uncertainty models are well-studied and commonly used, they may show some incapableness in fully characterizing model uncertainties for certain cases. Therefore, we introduce the uncertainty quartet. It combines the additive, multiplicative, subtractive and divisive uncertainty in a unified framework, so as to depict a wider range of uncertainties.

An elementary polynomial approach, with its aims to obtain the optimal controller that maximizes the so-called robust stability margin, is developed under the proposed uncertainty scheme. It shares the same interpretation with the conventional method in solving the optimal Nehari approximation problem, but with significantly reduced computational efforts since it only involves rudimentary polynomial and matrix manipulations.

Experimental studies of stabilizing an under-sensed and under-actuated linear (USUAL) inverted pendulum and a linear magnetic levitation system are also investigated. The results fully suggest the effectiveness and application potential of the proposed polynomial approach. We envision that the clarity and simplicity of our algorithm will help popularize the robust control theory in engineering applications.