Interval analysis and design of robust pole assignment controllers

The problem of synthesizing robust pole placement controllers for interval linear time-invariant plants is addressed in the context of the concepts and methods of interval analysis. The robust pole placement design problem is associated with the solution of an interval Diophantine equation, whose basic properties axe analyzed. Robust pole placement controllers axe viewed as inner solutions of the interval Diophantine equation. Simple and computationally efficient characterizations of the set of all robust pole placement controllers are then obtained and some of its geometric properties, discussed. Several aspects of the design of robust controllers by interval analysis are integrated into a linear goal programming formulation, which can also incorporate additional constraints on the controller parameters. Robust pole placement design problems are easily modeled and solved through the approach proposed. Numerical examples illustrate its main characteristics.