Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item Absolute Stability Theory, Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation(1997) Chou, Y.S.; Tits, A.L.; Balakrishnan, V.; ISRThe main contribution of the paper is to show the equivalence between the following two approaches for obtaining sufficient conditions for the robust stability of systems with structured uncertainties: (i) apply the classical absolute stability theory with multipliers; (ii) use the modern theory, specifically, the upper bound obtained by Fan, Tits and Doyle [IEEE TAC, Vol. 36, 25-38]. In particular, the relationship between the stability multipliers used in absolute stability theory and the scaling matrices used in the cited reference is explicitly characterized. The development hinges on the derivation of certain properties of a parameterized family of complex LMIs (linear matrix inequalities), a result of independent interest. The derivation also suggests a general computational framework for checking the feasibility of a broad class of frequency- dependent conditions, and in particular, yields a sequence of computable ﲭixed- -norm upper bounds , defined with guaranteed convergence from above to the supremum over frequency of the aforementioned upper bound.Item Robustness under Bounded Uncertainty with Phase Information(1996) Tits, A.L.; Balakrishnan, V.; Lee, Li; ISRWe consider uncertain linear systems where the uncertainties, in addition to being bounded, also satisfy constraints on their phase. In this context, we define the ﲰhase-sensitive structured singular value (PS-SSV) of a matrix, and show that sufficient (and sometime necessary) conditions for stability of such uncertain linear systems can be rewritten as conditions involving PS-SSV. We then derive upper bounds for PS-SSV, computable via convex optimization. We extend these results to the case where the uncertainties are structured (diagonal or block-diagonal, for instance).Item Globally Convergent Algorithms for Robust Pole Assignment by State Feedback(1995) Tits, A.L.; Yang, Y.; ISRIt is observed that an algorithm proposed in 1985 by Kautsky, Nichols and Van Dooren (KNV) amounts to maximize, at each iteration, the determinant of the candidate closed-loop eigenvector matrix X with respect to one of its columns (with unit length constraint), subject to the constraint that it remains a valid closed-loop eigenvector matrix. This interpretation is used to prove convergence of the KNV algorithm. It is then shown that a more efficient algorithm is obtained if det (X) is concurrently maximized with respect to two columns of X, and that such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs. Variations exploiting the availability of multiple processors are suggested. Convergence properties of the proposed algorithms are established. Their superiority is demonstrated numerically.Item When is the Multiaffine Image of a Cube a Polygon?(1992) Tsing, N-K.; Tits, A.L.; ISRWe give two simple sufficient conditions under which the multiaffine image on the complex plane of an m-dimensional cube is a convex polygon. A third condition which, in some generic sense, is necessary and sufficient is then obtained. The conditions involve checking the locations of the image of the vertices of the cube. These results help determine whether a family of parametrized polynomials is stable, and provide a tool for robust control analysis.Item On Continuity/Discontinuity in Robustness Indicators(1991) Lee, Li; Tits, A.L.; ISRContinuity/discontinuity of robustness indicators is reviewed. For the case of real or mixed uncertainty, a regularization of the frequency dependent robustness margin is proposed and its properties are discussed. Implication of this regularization in the case of polynomial families with affine dependency on the uncertainty is pointed out.Item A Measure of Worst-Case HPerformance and of Largest Acceptable Uncertainty(1991) Fan, Michael K-H.; Tits, A.L.; ISRThe structured singular value (SSV or ) is know to be an effective tool for assessing robust performance of linear time- invariant models subject to structured uncertainty. Yet all a single analysis provides is a bound ݠon the uncertainty under which stability as well as Hperformance level of k/ݠare guaranteed, where k is preselectable. In this paper, we introduce a related quantity, denoted by v which provides answers for the following questions: (i) given ݬ determine the smallest with the peoperty that, for any uncertainty bounded by ݬ an H performance level ofItem Linear Fractional Transformations for the Approximation of Various Uncertainty Sets(1991) Lee, Li; Tits, A.L.; ISRRecently, it was shown that the structured singular value framework can be extended to the case when information on the phase of the uncertainty is available, and a computable upper bound on the corresponding "phase sensitive structured singular value" was obtained. Here we show that the same bound can be obtained via an entirely different approach, using a family of linear fractional transformations. Extension to various uncertainty "shapes" follows.Item On Phase Information in Multivariable Systems(1991) Lee, Li; Tits, A.L.; ISRThe "median phase" and "phase spread" of a matrix are defined and properties are derived. The question of robust stability under uncertainty with phase information is addressed and a corresponding necessary and sufficient condition is given. This condition involves a "phase sensitive singular value". A computable upper bound to this quantity is obtained. The case when the uncertainty is block-structured is also considered.Item Worst-Case HPerformance Under Structured Perturbations with Known Bounds(1990) Fan, Michael K-H.; Tits, A.L.; ISRThe structured singular value (SSV or ) is known to be an effective tool for assessing robust performance of linear time- invariant models subject to structured uncertainty. Yet all a single analysis provides is a bound ݠon the uncertainty under which stability as well as Hperformance level of k/ݠare guaranteed, where k is reselectable. In this paper, we introduce a related quantity, denoted by v which, for a given ݬ provides a value such that for any uncertainty bounded by ݠan H performance level of ( but none better than ) is guaranteed.