There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

Multiple-input multiple-output (MIMO) technology is maturing and is being incorporated into emerging wireless broadband standards like long-term evolution (LTE) [1]. For example, the LTE standard allows for up to eight antenna ports at the base station. Basically, the more antennas the transmitter/receiver is equipped with, and the more degrees of freedom that the propagation channel can provide, the better the performance in terms of data rate or link reliability. More precisely, on a quasi static channel where a code word spans across only one time and frequency coherence interval, the reliability of a point-to-point MIMO link scales according to Prob(link outage) ` SNR-ntnr where nt and nr are the numbers of transmit and receive antennas, respectively, and signal-to-noise ratio is denoted by SNR. On a channel that varies rapidly as a function of time and frequency, and where circumstances permit coding across many channel coherence intervals, the achievable rate scales as min(nt, nr) log(1 + SNR). The gains in multiuser systems are even more impressive, because such systems offer the possibility to transmit simultaneously to several users and the flexibility to select what users to schedule for reception at any given point in time [2].

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Scaling Up MIMO: Opportunities and Challenges with Very Large Arrays

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

The authors determine conditions under which a diagonal dynamic precompensation is sufficient to achieve vector relative degree for multivariable nonlinear systems and describe a simple algorithm which determines such compensation. It is shown that the decouplability question is essentially associated with the nonsingularity or (non)generic singularity of a certain matrix related to the system. >

Dynamic decoupling of MIMO systems: nonlinear case

We propose a robust interpolation algorithm for model-based spectral estimation. The interpolation data represent information about the half spectrum function associated with a given signal and are computed from an input-to-state filter. Our algorithm allows a large number of noisy interpolation data to be used to optimally fit a half spectrum function of a fixed order. The algorithm involves solving a set of linear matrix inequalities and is thus numerically efficient.

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A Robust Interpolation Algorithm for Spectral Estimation

The stability of the inverse of the optimum forward prediction error filter obtained when the input data is nonstationary is investigated. Due to this nonstationary character, the resulting system (which is obtained assuming optimality on a sample-by-sample basis) is time-varying. It turns out that an extension of the Levinson recursion still provides a means to order-update the prediction error filters, leading to asymmetric lattice realizations of the filters. Sufficient conditions on the input process are given in order to ensure exponential asymptotic stability of the corresponding inverse system. Thus this work extends the well-known result from linear prediction theory which states that the transfer function of the optimum forward prediction error filter for a stationary process is minimum phase.

Stability conditions for the time-varying linear predictor

This paper presents a new distributed power-efficient method consisting of clock synchronization achieving and maintaining protocols. The achieving protocol can realize synchronization of time variations and initial time errors independently and simultaneously with an energy-efficient communication scheme designed in the paper. Then a stopping criterion is proposed to degrade the protocol into a maintaining one which is synthesized under the general strongly connected digraph to achieve more energy conservation. Numerical simulations are given to illustrate the performance of the method.

A new power-efficient distributed method for clock synchronization in sensor networks

The paper improves the cross-correlation method about the condition monitoring for train suspension systems. The faults of both the spring and the damper are discussed and the improved technique helps quantify the result of the detection in a great accuracy. A side-view model of the vehicle is employed and the simulation verifies the effectiveness of this method.

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Minyue Fu

Papers

Dynamic decoupling of MIMO systems: nonlinear case

A Robust Interpolation Algorithm for Spectral Estimation

Stability conditions for the time-varying linear predictor

A new power-efficient distributed method for clock synchronization in sensor networks

Condition monitoring for train suspension system based on cross-correlation