Stabilization of linear systems with fixed order controllers
The paper is concerned with the problem of stabilizing a linear time- invariant plant via output feedback. Existing techniques aiming at pole placement ususally require high order controllers of the type of a Luenberger observer. The paper suggests a method which allows construction of low order controllers if only stabilization is desired. To this end the coefficients of the pth order controller transfer function are mapped on the coefficients of the characteristic polynomial of the resulting closed-loop system. Linear programming techniques are applied for successive selection of Hurwitz polynomials to make the largest stability hypersphere intersect a linear subspace determined by the plant parameters and the order of the controller. Occurence of such an intersection by successively updating the order of the controller is sufficient for stabilizability. Numerical examples demonstrate that a controller with order far less than that of a pole placement controller can be obtained.
scientific article; zbMATH DE number 4029410
scientific article