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.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

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://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2002/data/content/02769/2769.pdf

Application of generalized sampled-data hold functions to decentralized control structure modification

http://ieeexplore.ieee.org/iel5/9/24098/01098756.pdf

Controllability of a class of nonlinear time-variable systems

Control of pH in a Continuous Stirred Tank Reactor (CSTR)

In this paper, an efficient algorithm is presented for solving the 2-D optimization problem which is associated with computing the robustness measures of a number of linear time-invariant (LTI) system properties such as the controllability radius, the decentralized fixed-mode radius, and the minimum-phase radius. Unlike methods such as gradient search methods, the proposed algorithm works well independent of the initial trial point, and obtains the minimum with a high level of confidence that it is indeed global. A numerical example is included.

A fast algorithm to compute the controllability, decentralized fixed-mode, and minimum-phase radius of LTI systems

The problem of regulating the temperature of a large multi-zone building to specified constant set-points, subject to arbitrary constant external/internal heat sources, by using partial decentralized control is considered in this paper. Existence conditions for a solution to exist and a characterization of controllers which solve the problem are given. In particular, it is shown that if in controlling a particular zone, a controller is allowed to use sensor outputs from its immediate neighbouring zones, then a solution to the problem can always be achieved. It is also shown that such a controller can be designed without requiring a detailed mathematical model of the process to be available, i.e. by using tuning regulator methods [10], [11]. The controller is therefore believed to be quite realistic to implement.

Edward J. Davison

Papers

Application of generalized sampled-data hold functions to decentralized control structure modification

Controllability of a class of nonlinear time-variable systems

Control of pH in a Continuous Stirred Tank Reactor (CSTR)

A fast algorithm to compute the controllability, decentralized fixed-mode, and minimum-phase radius of LTI systems

Partial decentralized temperature control of multi-zone buildings