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Controller design for slowly varying interval plants using gain scheduling and interval mathematics

Interval analysis techniques are well known in the mathematics literature, but have found few applications in control engineering. We develop a new methodology for robust pole region assignment using interval analysis. We apply the new methodology to the control of nonlinear system with slowly varying dynamics using gain-scheduling. We derive sufficient conditions for the poles of a linear system of known interval uncertainty bounds to remain in a specified region. We also derive sufficient conditions for a nonlinear system with gain-scheduled control to achieve the desired dynamics using a limited number of design points and linear interpolation. A design algorithm is provided and an example is given to demonstrate the process.