Solvability Condition for a Class of Parametric Robust Stabilization Problem

The robust stabilization problem (RSP) for a plant family P(s,δ,δ) having real parameter uncertainty δ will be tackled. The coefficients of the numerator and the denominator of P(s,δ,δ) are affine functions of δ with ‖δ‖p≤δ. The robust stabilization problem for P(s,δ,δ) is essentially to simultaneously stabilize the infinitely many members of P(s,δ,δ) by a fixed controller. A necessary solvability condition is that every member plant of P(s,δ,δ) must be stabilizable, that is, it is free of unstable pole-zero cancellation. The concept of stabilizability radius is introduced which is the maximal norm bound for δ so that every member plant is stabilizable. The stability radius δmax(C) of the closed-loop system composed of P(s,δ,δ) and the controller C(s) is the maximal norm bound such that the closed-loop system is robustly stable for all δ with ‖δ‖p <δmax(c). using the convex parameterization approach it is shown that maximal stability radius exactly stabilizability radius. therefore, rsp solvable if and only every member plant of p(s,δ,δ) stabilizable.< div>

Keywords:
• parameter uncertainty,
• parametric robust stabilization,
• stabilizability radius,
• stability radius,
• convex parameterization approach