by Michael Athans. / Bibliography: leaf [3]. / "August 1983." / Supported by the Office of Naval Research under Grant ONR/N00014-82-K-0582 NR 606-003 NASA Ames and Langley Research Centers under Grant NGL-22-009-124

CAPES / O objetivo desta dissertação é propor uma técnica para a síntese via realimentação de estados para sistemas lineares e invariantes no tempo, considerando que os estados realimentados são previamente quantizados. Para tanto, o erro de quantização é inicialmente modelado como um ruído externo. Assim, o problema de obter os ganhos de realimentação de estados, se torna um problema de projetar os ganhos que minimizem a norma H¥ do sistema controlado. Os ganhos de realimentação são calculados pela solução de um conjunto de condições descritas na forma de desigualdades matriciais lineares. A técnica é ilustrada pela aplicação da realimentação de estados quantizada em um servomecanismo. / The main objective of this dissertation is to propose a technique for synthesis by statefeedback for linear time-invariant systems, considering that the states are quantized before the feedback. To tackle such problem, the quantization error is initially modeled as an external noise. Therefore, the problem of getting the state-feedback gains, becomes a problem of designing the gains that minimize the H¥ norm of the system. The state-feedback gains are calculated by solving a set of conditions described in the form of linear matrix inequalities. The technique is illustrated by applying the of feedback of quantized states to a servo-mechanism.

CAPES / O objetivo desta dissertação é propor uma técnica para a síntese via realimentação de estados para sistemas lineares e invariantes no tempo, considerando que os estados realimentados são previamente quantizados. Para tanto, o erro de quantização é inicialmente modelado como um ruído externo. Assim, o problema de obter os ganhos de realimentação de estados, se torna um problema de projetar os ganhos que minimizem a norma H¥ do sistema controlado. Os ganhos de realimentação são calculados pela solução de um conjunto de condições descritas na forma de desigualdades matriciais lineares. A técnica é ilustrada pela aplicação da realimentação de estados quantizada em um servomecanismo. / The main objective of this dissertation is to propose a technique for synthesis by statefeedback for linear time-invariant systems, considering that the states are quantized before the feedback. To tackle such problem, the quantization error is initially modeled as an external noise. Therefore, the problem of getting the state-feedback gains, becomes a problem of designing the gains that minimize the H¥ norm of the system. The state-feedback gains are calculated by solving a set of conditions described in the form of linear matrix inequalities. The technique is illustrated by applying the of feedback of quantized states to a servo-mechanism.

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The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones. This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity. In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order can be reduced even further. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems. The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results. In the last part of the thesis, topics for future investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific and time-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects. / Series: Working Papers in Regional Science

This dissertation focuses on wideband circuit design and implementation issues up to 10GHz based on the direct conversion architecture in the CMOS and SiGe BiCMOS technologies. The dissertation consists of two parts: One, implementation of a RF front-end receiver for an ultra-wideband system and, two, implementation of a local oscillation (LO) signal for a GSM/WCDMA multiband application. For emerging ultra-wideband (UWB) applications, the key active components in the RF front-end receiver were designed and implemented in 0.18um SiGe BiCMOS process. The design of LNA, which is the critical circuit block for both systems, was analyzed in terms of noise, linearity and group delay variation over an extemely wide bandwidth. Measurements are demonstrated for an energy-thrifty UWB receiver based on an MB-OFDM system covering the full FCC-allowed UWB frequency range. For multiband applications such as a GSM/WCDMA dual-band application, the design of wideband VCO and various frequency generation blocks are investigated as alternatives for implementation of direct conversion architecture. In order to reduce DC-offset and LO pulling phenomena that degrade performance in a typical direct conversion scheme, an innovative fractional LO signal generator was implemented in a standard CMOS process. A simple analysis is provided for the loop dynamics and operating range of the design as well as for the measured results of the factional LO signal generator.

This thesis investigates the frequency weighted balanced model reduction problem for linear time invariant systems. Both continuous and discrete time systems are considered, in one and two-dimensions. First the frequency weighted balanced model reduction problem is formulated, then a novel frequency weighted, balanced, model reduction method for continuous time systems is proposed. This method is based on the retention of frequency weighted Hankel singular values of the original system, and yields stable reduced order models even when two sided weightings are employed. An alternative frequency weighted balanced model reduction technique (applicable for controller reduction applications) is then developed. This is based on a parametrized combination of the frequency weighted partial fraction expansion technique with balanced truncation and the singular perturbation approximation techniques. This method yields stable models even when two sided weightings are employed. An a priori error bound for the model reduction method is derived. Lower frequency response errors and error bounds are obtained using free parameters and equivalent anti-stable weightings. Based on the same idea, a novel parameterized frequency weighted optimal Hankel norm model reduction method with a tighter a priori error bound is proposed. The proposed methods are extended to include discrete time systems. A frequency interval Gramians based stability preserving model reduction scheme with error bounds is also presented. In this case, frequency weights are not explicitly predefined. Discrete time system related results are also included. Several frequency weighted model reduction results for two-dimensional (2-D) systems are also proposed. The advantages of these schemes include error bounds, guaranteed stability and applicability to general stable (non-separable denominator) weighting functions. Finally, a novel 2-D identification based frequency weighted model reduction scheme is outlined. Numerically robust algorithms based on square root and balancing free techniques are proposed for frequency weighted balanced truncation techniques. Several practical examples are included to illustrate the effectiveness of the algorithms.

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects. / Series: Working Papers in Regional Science