Controller Design With Regional Pole Constraints : Hyperbolic and Horizontal Strip Regions

In this paper we consid~r the des~gn of robust controllers with closed-loop poles constrained to lie in specified regions in the left half complex plane The paper focuses In part~cular on hyperbolic and horizontal strip regions The hyperbolic region places a lower bound on the damping ratio whereas the horizontal strip region places an upper bound on the natural frequency of the closed-loop system. Each con-stramt reglon is characterized by a paw of matrix root-clustering equations These equations, wh~ch govern the response of the closed-loop system, are utilized in conjunction wlth a steady st at,e quadratic performance criterion By applying fixed-structure synthesis tech-nlques, we obtain feedback controllers that achieve the desired performance properties along with suboptimal closed-loop performance. Nomenclature real numbers, m x 1 real matrices complex numbers, m x 1 complex matrires expectation, trace operator T x T identity matrix Kronecker product, Kronecker sum, n x n permutation matrix; as defined in Ref. 12 spectrum of A , complex conjugate of A E C n, m, 1 and n,-dimensional vectors d-dimensional standard white noise n x n , n x m and 1 x n dimensional matrices n x d, 1 x d and m x 1 dimensional matrices