Feedback Controller Design for Simultaneous Stabilization. Methods to Construct Simultaneously Stabilizing Controllers and Rational Polynomials with Interpolation Constraints

      Аннотация: This book enlarges the class of systems, for which a simultaneously stabilizing controller can be designed, and restricts the class of controllers, from which a solution must exist. The new results here apply to the output feedback stabilization of linear, time invariant, continuous time, single-input, single-output plants. New necessary and sufficient conditions require the existence of an exactly proper controller. For the two plant case, necessary and sufficient conditions are derived only in terms of the plant parameters eliminating the use of the Bezout Identity in determining the existence and the construction of the controller. New sufficient conditions stabilize non-minimum phase plants and relax the high frequency sign condition for minimum phase plants. A new interpolation algorithm is used to create bounded real minimum phase rational polynomials of finite order in constructing simultaneously stabilizing controllers. Generalized sufficient conditions reduce in special cases to results published by several authors. Proofs are constructive so the controllers can be designed, when these new sufficient conditions are satisfied. Examples illustrate the new results.

Ключевые слова: Interpolation, Compensator, control system theory, simultaneous stabilization, bounded real unit, rational polynomial, exactly proper, strictly proper, parity interlacing property, Positive Definite, nevanlinna-pick interpolation, finite order controller, exactly interpolating unit, positive semi-definite, stable controller, H Infinity, Bezout Identity, multiple interpolations, positive real, positive analytic, Hurwitz stable, high frequency sign, minimum order, Mapping, transform, Operator, Proof by Construction, minimum phase controller, unit controller, strong stabilization, Control Systems, polynomial, plants, Controller, stable, bounded, stabilizable, strongly stabilizable, bounded real, Proper, proper plant, exactly proper plant, strictly proper controller, strictly proper plant, difference plant, difference plants, nevanlinna-pick, nevanlinna-pick matrix, nevanlinna-pick testing matrix, finite order, finite order compensator, finite order polynomial, exact interpolation, exactly interpolating, H infty, Bezoot Identity, interpolations, Hurwitz polynomial, same high frequency sign, common high frequency sign, finite interpolations, interpolation at infinity, simple finite interpolations, Constructive Proof, minimum phase, minimum phase compensator, minimum phase plant, Hurwitz numerator, Hurwitz denominator, unit compensator, unit stabilization, strongly stabilizing, strongly stabilizing controller, strongly stabilizing compensator, controls, avoidance, Intersection, Transfer Function, constructing polynomials, Nth Root, nth power, closed loop transfer function, CLTF, common zeros, common intersections, right half plane, RHP, constructing controllers, constructing compensators, designing controllers, designing compensators, avoiding intersections