Full Download On Structured Singular Values (Classic Reprint) - James Demmel | ePub
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We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility sdp and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks.
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Introductionstructured singular values and pseudospectra are useful tools for analyzing the spectral behavior of matrices and dynamical systems under uncertainties. Given a class of perturbations ∆ ⊆ c n×n, the structured singular value of a matrix b ∈ c n×n is defined as here and in the following, denotes the 2-norm (also called spectral norm) of a matrix.
Real structured singular values and real structured pseudospec-tra, respectively. In particular, an algorithm is developed that computes the real pseudospectrum at a cost of o(n2) operations per grid point. These results are extended to skew-symmetric, hermitian, and hamiltonian pseudospectra in sections 4, 5, and 6, respectively.
Controlling the singular values of n-dimensional matrices is often sdp solvers are still not as mature as more classical convex opti- underlying structure.
The structured singular value (ssv) [1] is an important and versatile tool in control, as it allows to address a cen-tral problem in the analysis and synthesis of control systems. To quantify the stability of a closed-loop linear time-invariant systems subject to structured perturbations. The class of structures addressed by the ssv is very general.
The singular value decomposition (svd) goes back to the beginning of this century. Following classical result allows us to simplify this expression considerably and the largest structured singular value of an n × n complex matrix.
The structured singular value was introduced independently by doyle and safanov as a tool for analyzing robustness of system stability and performance in the presence of structured uncertainty in the system parameters.
In this article, the computation of μ-values known as structured singular values ssv for the companion matrices is presented.
Classical golub-kahan method for computing the singular value complex symmetric tridiagonal matrix as intermediate matrix structure and combining this with.
Aspects of real and complex-structured singular-value analysis. A general concept which is very useful for norm- bounded uncertainty modelling, and especially for robustness analysis with the structured singular value, is the linear fractional transformation (lft).
Putes the structured singular value decomposition of real or complex symyplectic in the classical jacobi method, the pivot in step i is the largest off-diagonal.
Structured singular values and pseudospectra are useful tools for analyzing the spectral behavior of matrices and dynamical systems under uncertainties.
Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization, including the classes of real, skew-symmetric, hermitian.
This matlab function calculates upper and lower bounds on the structured singular value, or µ, for a given block structure.
Robustness, structured singular values ofier the advantage of measuring the robustness of speciflc biological performances to multiple, simultaneous parametric perturbations. In this paper, the fas-induced apoptosis network, whose failure has been cited in several forms of cancer [14], is analyzed for robust stability to parametric uncertainty.
We introduce the structured singular value μ and discuss its use as an analysis tool for flight control applications. To apply μ-analysis tools to flight control law clearance problems, linear fractional transformation (lft) based uncertainty models must first be generated to capture the effect of uncertain aircraft parameters on the closed-loop system dynamics.
Symbolic differentiation for fixed-structure controller synthesis.
The paper discusses an extension of \mu (or structured singular value), a well-established technique from robust control for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems.
The singular value decomposition can be viewed as a way of but there is more structure lurking in these matrices.
Structured singular value tools and the v gap metric c'huanjiang zhu major professors: vijay yittal and mustafa k ham mas h iowa state university modern power systems are operated more stressed than ever because of the advent of deregulation and competition.
We describe an interior point algorithm for computing the upper bound for the structured singular value described in the paper by fan, tits and doyle, ieee trans.
Jan 28, 2005 framework provided by singular value decomposition (svd). Quantitative measures the approach enables analysis of the control structure over a range of a classical/modern synthesis,” ieee trans.
03 engr210a lecture 18: the structured singular value structure speci cations lti uncertainty parametric uncertainty the structured singular value upper and lower bounds the matrix structured singular value computation.
May 3, 2012 singular values of the perturbed matrix differs from that of the original matrix if and only the following proposition allows us to assert that in many classical matrix hermitian structure, are bounded independentl.
Application of real structured singular values to flight control law validation miotto, piero;.
Structured singular values (µ), each local area controller can be designed independently such that stability of the overall closed loop system is guaranteed. The robust sta-bility condition for the overall system can be easily stated as to achieve a sufficient interaction margin, and a suf-ficient gain and phase margins during each.
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