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

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

From the Publisher:
A comprehensive treatment of model-based fuzzy control systems
This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications.
Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model.
This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field.
Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

Linear controller design: limits of performance

A computer-aided design (CAD) method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results that parameterize all controllers that stabilize a given plant. With this architecture, the design of controllers is a convex programming problem that can be solved numerically. Constraints on the closed-loop system, such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response, settling time, and overshoot, as well as frequency-domain inequalities, are readily incorporated in the design. The minimization objective is quite general, with LQG (linear quadratic Gaussian) H/sub infinity / and new l/sub 1/ types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on. >

A new CAD method and associated architectures for linear controllers

A wireless system includes a network of base stations (1) for receiving uplink signals transmitted from a plurality of remote terminals (69) and for transmitting downlink signals to the remote terminals. Each base station (1) includes a plurality of transmitting antenna elements (18) for transmitting downlink signals and receiving antenna elements (19) for receiving uplink signals, a signal processor (13) connected to the antenna elements for determining spatial signatures and multiplexing and demultiplexing functions. A multiple base station controller (66) is used for optimizing network performance.

Spectrally efficient high capacity wireless communication systems

A wireless system comprising a network of base stations (1) for receiving uplink signals transmitted from a plurality of remote terminals and for transmitting downlink signals to the remote terminals using a plurality of channels including a plurality of antenna elements (19) at each base station for receiving uplink signals, a plurality of antenna elements (18) at each base station for transmitting downlink signals, a signal processor (13) at each base station connected to the receiving antenna elements (19) and to the transmitting antenna elements (18) for determining spatio-temporal multiplexing and demultiplexing functions for each remote antenna for each channel, and a multiple base station network controller for optimizing network performance, whereby communication between the base stations and the remote terminals in each channel can occur simultaneously.

Spectrally efficient high capacity wireless communication systems with spatio-temporal processing

A method operating in a communications station for calibrating the communications station, the communications station including an antenna array of antenna elements, each having associated with it and included in a transmit apparatus chain and a receiver apparatus chain. The method comprises transmitting a prescribed signal from each antenna element using the transmit apparatus chain associated with the antenna element while receiving the transmitted signal in receiver apparatus chains not associated with the antenna. Calibration factors for each antenna element are determined as dependent on the associated transmit apparatus chain and receiver apparatus chain transfer functions using the prescribed signal and each of the signals received during transmissions. A communications station also is described which includes: an antenna array of a plurality of elements, each antenna element having associated with it and included in a transmit apparatus chain and a receiver apparatus chain; transmitting means configured to transmit a prescribed signal from each antenna element while receiving the transmitted signal in at least one receiver apparatus chain not associated with the transmitting antenna element; a memory coupled to the receiver apparatus chains for storing the signals received during the transmissions of the prescribed signals; and a signal processor coupled to the memory and configured to determine calibration factors for each antenna element, the calibration factors for a particular antenna element based on the transmit apparatus chain and receiver apparatus chain transfer functions of the transmit and receiver apparatus chains, respectively, that are associated with the particular antenna element.

Craig H. Barratt

Papers

Linear controller design: limits of performance

A new CAD method and associated architectures for linear controllers

Spectrally efficient high capacity wireless communication systems

Spectrally efficient high capacity wireless communication systems with spatio-temporal processing

Method and apparatus for calibrating radio frequency base stations using antenna arrays