Robust SPR Synthesis for Low-Order Polynomial Segments and Interval Polynomials
نویسندگان
چکیده
We prove that, for low-order (n ≤ 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson’s claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for low-order interval polynomials is also discussed.
منابع مشابه
Geometric Characterization of Strictly Positive Real Regions and Its Applications
Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real (SPR) regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a ...
متن کامل. O C ] 2 3 Fe b 20 02 GEOMETRIC CHARACTERIZATION OF STRICTLY POSITIVE REAL REGIONS AND ITS APPLICATIONS
Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real (SPR) regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a ...
متن کاملPhase-Convex Arcs in Root Space and Their Application to Robust SPR Problem
This paper considers the problem of identifying regions in the complex-plane, such that polynomials having roots in those regions, have their phase bounded by that of a few extreme polynomials. We present suÆcient and testable conditions for dis erent regions satisfying this property. Applications of the results to the robust SPR analysis and synthesis problems are illustrated.
متن کاملOn the synthesis of robust strictly positive real discrete-time systems
The Strict Positive Real (SPR) property of discrete-time transfer functions plays a fundamental role in the analysis of the behaviour of several recursive schemes employed in identification and adaptive control. In the context of uncertain systems, this leads to the so called robust SPR problem (RSPR), i.e., given a set P of polynomials and a region Λ of the complex plane, determine, provided i...
متن کاملAlgebraic solution to the robust SPR problem for two polynomials
In this paper we provide an algebraic method for the design of an appropriate transfer function making simultaneously two polynomials strictly positive real (SPR), in the so-called robust SPR problem for two polynomials. This problem arises in the design of recursive estimation algorithms used for identi"cation purposes and in active noise control (ANC) applications. In the former a given trans...
متن کامل