Parameter space design of robust control systems

Find a state or output feedback with fixed gains such that nice stability (defined by a region in the eigenvalue plane) is robust with respect to large plant parameter variations, sensor failures, and quantization effects in the controller. Keep the required magnitude of control inputs small in this design. A tool for tackling such problems by design in the controller parameter space is introduced. Pole placement is formulated as an affine map from the space of characteristic polynomial coefficients to the space. This allows determining the regions in the space, which place all eigenvalues in the desired region in the eigenvalue plane. Then tradeoffs among a variety of different design specifications can be made in space. The use of this tool is illustrated by the design of a crane control system. Several open research problems result from this approach: graphical computer-aided design of robust systems, algebraic robustness conditions, and algorithms for iterative design of robust control systems.