### Browsing by Author "Saydy, L."

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Item Asymptotic Behavior in Nonlinear Stochastic Filtering(1987) Saydy, L.; Blankenship, G.L.; ISRA lower and upper bound approach on the optimal mean square error is used to study the asymptotic behavior of one dimensional nonlinear filters. Two aspects are treated: (1) The long time behavior (t Ġ. (2) The asmptotic behavior as a small parameter Ġ0. Lower and upper bounds that satisfy Riccati equations are derived and it is shown that for nonlinear systems with linear limiting systems, the Kalman filter designed for the limiting systems is asymptotically optimal in a reasonable sense. In the case of nonlinear systems with low measurement noise level, three asymptotically optimal filters are provided one of which is linear. In chapter 4, the stationary behavior of the Benes filter is investigated.Item Asymptotic Behavior in Nonlinear Stochastic Filtering.(1987) Saydy, L.; Blankenehip, Gilmer L.; ISRA lower and upper bound approach on the optimal mean square error is used to study the asymptotic behavior of one dimensional nonlinear filters. Two aspects are treated: (1) The long time behavior (t --> INFINITY). (2) The asymptotic behavior as a small parameter EPSILON-->0. Lower and upper bounds that satisfy Riccati equations are derived and it is shown that for nonlinear systems with linear limiting systems, the Kalman filter designed for the limiting systems is asymptotically optimal in a reasonable sense. In the case of nonlinear systems with low measurement noise level, three asymptotically optimal filters are provided one of which is linear. In chapter 4, the stationary behavior of the Benes filter is investigated.Item A Bound Approach to Asymptotic Optimality in Nonlinear Filtering of DifFusion Processes.(1987) Saydy, L.; Blankenehip, Gilmer L.; ISRThe asymptotic behavior as a small parameter EPSILON --> 0 is investigated for one dimensional nonlinear filtering problems. Both weakly nonlinear systems (WNL) and systems measured through a low noise channel are considered. Upper and lower bounds on the optimal mean square error combined with perturbation methods are used to show that, in the case of WNL, the Kalman filter formally designed for the underlying linear systems is asymptotically optimal in some sense. In the case of systems with low measurement noise, three asymptotically optimal filters are provided, one of which is linear. Examples with simulation results are provided.Item Maximal Range for Generalized Stability- Application to Two Physically Motivated Examples.(1989) Saydy, L.; Tits, A.L.; Abed, Eyad H.; ISRSome recent results on guardian maps and their application to generalized robust stability are reviewed and a characterization of the maximum stability range is obtained. This framework is then applied to the analysis of robust stability in two physically motivated examples.Item On Robust Eigenvalue Location.(1989) Tits, A.L.; Saydy, L.; ISRThe concepts of guardian and semiguardian maps were recently introduced as tools for assessing robust generalized stability of parametrized families of matrices or polynomials. Necessary and sufficient conditions were obtained for stability of parametrized families with respect to a large class of open subsets of the complex plane, namely those with which one can associate a polynomic guardian or semiguardian map. This note focuses on a class of disconnected subsets of the complex plane, of interest in the context of dominant pole assignment and filter design. It is first observed that the robust stability conditions originally put forth are in fact necessary and aufficient for the number of eigenvalues (matrices) or zeros (polynomials) in any given connected component to the same for all the members of the given family. Polynomic semiguardian maps are then identified for a class of disconnected regions of interest. These maps are in fact "essentially guarding with respect to one-parameter families."Item On Stabilization with a Prescribed Region of Asymptotic Stability.(1988) Saydy, L.; Abed, Eyad H.; Tits, A.L.; ISRAn important unsolved problem in nonlinear control is that of stabilization with a prescribed region of stability. In this paper, sufficient conditions are obtained for the existence of a linear feedback stabilizing an equilibrium point of a given nonlinear system with the resulting region of asymptotic stability (RAS) containing a ball of given radius. Conditions for global stabilization are also given. Feedback stabilization is achieved while satisfying a certain robustness property. The technique is applied to planar systems, resulting in a complete design methodology for this case. Examples and simulations illustrating the method are presented.Item On the Generalized Stability of the Convex Hull of Two Matrices.(1988) Saydy, L.; Tits, A.L.; Abed, Eyad H.; ISRContingent on the existence of certain affine maps, necessary and sufficient conditions for the eigenvalues of all matrices belonging to the convex hull of two given matrices to lie in a subset of the complex plane are obtained. Such maps are identified for every balanced convex domain D with polygonal boundary and conclusive D-stability criteria are obtained. In the case when D is the open left half plane, the computational complexity of the new test is somewhat lower than that of a previously proposed criterion. For nonpolygonal balanced convex domains, conditions that are as close to being necessary and sufficient as desired may be obtained via a suitable approximation of these domains by polygonal ones.Item Optimal Stationary Behavior in Some Stochastic Nonlinear Filtering Problems- A Bound Approach.(1987) Saydy, L.; Blankenehip, Gilmer L.; ISRA lower and upper bound on the a priori optimal mean square error is used to study the stationary behavior of one dimensional nonlinear filters. The long time behavior as t--> INFINITY for asymptotically linear systems is investigated. Lower and upper bounds of the Riccati type are derived and it is shown that for nonlinear systems with linear limiting ones, the Kalman filter (KF) formally designed for the limiting systems is asymptotically optimal in some sense. Examples with simulation results are provided.Item Robust Stability of Complex Families of Matrices and Polynomials(1990) Saydy, L.; Tits, A.L.; Abed, Eyad H.; ISRRecently, the authors introduced the "guardian map" approach as a unifying tool in the study of robust generalized stability questions for marametrized families of matrices and polynomials. Real matrices and polynomials have been emphasized in previous reports on this approach. In the present note, the approach is discussed in the context of complex matrices and polynomials. In the case of polynomials, some algebraic connections with other recent work are uncovered.Item Robust Stability via the Guardian Map Approach: A Perspective(1990) Saydy, L.; Tits, A.L.; Abed, Eyad H.; ISRGuardian and semiguardian maps were recently introduced as tools for investigating generalized stability of parametrized families of matrices and of polynomials. Here we give a brief survey of the motivation and scope of application of the guardian and semiguardian map concepts.Item Studies in Robust Stability(1989) Saydy, L.; Abed, E.; Tits, A.; ISRIn this thesis, questions in the analysis and synthesis of stability robustness properties for linear and nonlinear control systems are considered. The first part of this work is devoted to linear systems., where the emphasis is on obtaining necessary and sufficient conditions for stability of parametrized families of systems. This class of robustness problems has recently received significant attention in the literature [1]. In the second part of the thesis, questions of stabilization of nonlinear systems by feedback are considered. Part I of this work addresses the generalized stability, i.e. stability with respect to a given domain in the complex plane, of parametrized families of linear time-invariant systems. The main contribution is the introduction and application of the new concepts of "guarding map" and "semiguarding map" for a given domain. Basically, these concepts allow one to replace the original parametrized system stability problem with a finite number of stability tests. Moreover, the tool is very powerful in that it allows the treatment of a large class of domains in the complex plane. The parametrized stability problem is completely solved for the case stability of a one- parameter family with respect to guarded and semiguarded domains. The primary interest in semiguarded domains arises in a process of reduction of a given multiparameter problem to one involving fewer parameters. For the two-parameter case, we consider stability of families of matrices relative to domains with a polynomial guarding map. The first step replaces the two- parameter problem by a one-parameter stability problem relative to a new domain. The second step employs a polynomial semiguarding map for the new domain to obtain necessary and sufficient conditions for stability of the new problem. The case of three or more parameters, which involves technical questions not encountered in the one- or two-parameter case, is also considered. In Part II, a class of nonlinear control systems for which the linear part satisfies special stabilizability conditions is considered. These conditions naturally give rise to certain nonstandard algebraic issues in linear systems. Sufficient conditions for the existence of a linear feedback control which stabilizes a given nonlinear control system within a prescribed ball of given radius (possibly infinite) are given. The feedback control is found to be robust in a certain sense against a class of modeling errors. A complete design methodology is obtained for planar systems and extended to a class of higher dimensional singularly perturbed nonlinear control systems. For these systems, nonlinear feedback laws achieving stabilization within prescribed cylindrical regions are presented.