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A robust analysis approach based on the computation of value set boundaries is presented. In the first part, the calculation of the boundary of regions corresponding to uncertain poles, zeros and delay plants is extended to more general parametric factorizable uncertain systems. In the second part, based on the Tree Structured Decomposition (TSD) concept, the operation (+,-,??,??) among boundaries...
The purpose of this paper is to establish a link between the structured singular value and the stability analysis of uncertain polynomials. We first give an analytical expression for a generalization of the structured singular value under a certain circumstance and next show how stability problems of uncertain polynomials may be studied in this framework. Our results include a number of small gain...
Recently, global convergence and parameter consistency of a certain parallel model adaptation algorithm in the presence of additive colored noise was established in [1]. In this paper, we examine the robustness of this algorithm, whose design is based on stochastic considerations, to bounded disturbances and unmodeled dynamics. We show that this algorithm is robust with respect to bounded disturbances...
Considering linear systems with uncertain real parameters appearing linearly in the characteristic polynomial, we introduce a new norm for column transfer functions, measuring the maximal norm of the real part along the imaginary axis. This allows less conservative robustness specifications than the H??, norm. In particular, we consider uncertainty in models from black box identification.
Associated with a polynomial p(s) and an interval ?? ?? R is a frequency response arc. This arc is obtained by sweeping the frequency ?? over ?? and plotting p(j??) in the complex plane. We say that an arc is proper if it does not pass through the origin and the net phase change of p(j??) for all ?? ?? ?? is no more than 180 degrees. In this paper, we establish convexity of all proper frequency response...
In this paper we solve the problem of robust stabilization for SISO systems with real linear-fractional parametric uncertainties. Perfect robust stabilization (PRS) is defined and its connection to 'strong stabilization' is shown. Conditions for PRS in various cases are given.
It is shown in this paper that the robust stability of a discrete-time system discribed by the delta-operator and whose characteristic polynomial has coefficients whose values lie in a box parallel to the axis, can be investigated using a minimum number of vertex polynomials. The number of vertex polynomials increases with the order of the system.
Robust approximation and identification of stable shiftinvariant systems is studied in the H∞ sense using a stable perturbation set-up. Issues of model set selection tion are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in the n-width sense. A general construction of interest to identification theory using ϵ-nets...
A new robust stability condition is derived for analyzing the robustness property of discrete-time two-parameter control systems with nonlinear time-varying uncertainties. Based on the concept of excess robustness and the theory of minimum H?? norm, a feasible and effect design algorithm is presented to synthesize a two-parameter robust controller which ensures that discrete-time two-parameter control...
In this paper Schur stability of discrete time uncertain control systems is investigated. It is shown that Schur stability of the control system is determined mainly by the stability of the exposed edges in the value set. A collinearity condition is derived which allows the determination of the changes in the exposed edges. Especially plants with symmetric/antisymmetric parametrization are considered...
A controller stabilizes an entire family of plants with affine uncertainty, if it simultaneously stabilizes a finite number of polynomials. An upper bound for this number is 4k.
In this paper, we study the envelope of the Nyquist plots generated by an interval plant family and show that this boundary is not always contained in the Nyquist plots of the Kharitonov plants. With this motivation, we give a sufficient condition for an envelope point to be contained in the Nyquist plot of a Kharitonov plant and use it to generate large and critical portions of the Nyquist envelope...
It has been shown that a first-order linear compensator stabilizes an interval plant with numerator and denominator being Kharitonov polynomials if and only if sixteen extreme plants are Hurwitz. The sixteen extreme plants are generated by using the four extreme polynomials of the numerator and the four extreme polynomials of the denominator corresponding to the maximum or minimum values of real or...
It has recently been shown that a first order compensator robustly stabilizes an interval plant family if and only if it stabilizes all of the extreme plants. That is, if the plant is described by m-th order numerator and monic n-th order denominator with coefficients lying in prescribed intervals, it is necessary and sufficient to stabilize the set of 2m+n+l extreme plants. These extreme plants are...
In this paper, we present some results related to the stability of polygons of real polynomials. These results are then used to test the stability of the two-dimensional exposed faces of a polytope of polynomials. The results are also used to give an alternative proof of the Edge Theorem.
In this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented. An objective function consisting on two terms is proposed, penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem. The algorithm is based...
The stability version of the Edge Theorem states that a polytope of polynomials is D-stable if and only if its edge polynomials are all D-stable. Unfortunately, this statement is only true for restricted classes of polytopes and restricted classes of stability regions. If either of these restrictions is removed, the theorem will not be valid. In order to remove these constraints, this paper will present...
In this paper, we review the partial realization problem (PRP) in an identification framework. Hence the use of erroneous Markov parameters in its solution is considered. The derived algorithm, which requires knowledge of the covariance matrix of these errors, allows to consistently estimate the coefficients of the characteristic polynomial, from which the system poles can be determined.
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