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

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

Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.

Variable structure systems with sliding modes

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

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

http://ieeexplore.ieee.org/iel5/9/24093/01098499.pdf

The stability of certain classes of differential equations

Traffic Congestion Control of Traffic Network

Control and Stabilization of Interconnected Dynamical Systems

In this paper, we consider the problem of designing a selltuning regulator for an unknown, asyrnptotically stable, linear, time-invariant, multivariable plant which will carry out asymptotic error regulation for all constant reference and disturbance signals and all plant initial conditions, while at the same time ensuring that the plant and the controller states remain bounded. In this problem only the plant output and the reference signal are used as controller inputs. It is not assumed that the plant order or the relative degree are known, or that the plant is minimum phase. The only assumptions made are that the plant is open loop asymptotically stable, that there exists a solution to the problem, and that an estimate of the steady-state DC gain matrix (easily obtainable by carrying out a finite number of experiments on the plant) is available when there are more than two outputs. A self-tuning regulator is presented which consists of a multivariable integral compensator together with a tuning mechanism which "tunes" the parameters of this compensator. It is shown that if the reference and disturbance inputs are constant, then the controller and the plant states remain bounded for all t, and asymptotic error regulation occurs. A number of simulation examples are included to illustrate the behaviour of the controller when applied to "unknown" plants.

The self-tuning robust servomechanism problem

In the design of a robust servomechanism system, it is well known that system cannot track a reference signal whose frequency coincides with the transmission zeros of the system. In this paper, we propose a new design method to overcome this difficulty. The controller to be used employs a sampler and holding device.

Edward J. Davison

Papers

The stability of certain classes of differential equations

Traffic Congestion Control of Traffic Network

Control and Stabilization of Interconnected Dynamical Systems

The self-tuning robust servomechanism problem

Penetrating transmission zeros in the design of robust servomechanism systems