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)

This paper generalizes the notion of real perturbation values of a complex matrix to account for a more general perturbation structure. Formulas for computing the so-called generalized real perturbation values of a matrix are derived and presented. Using these results, we revisit the computation of the structured real controllability radius that was previously used to evaluate the robustness of the multi-link inverted pendulum system, and we also study a new normalized version of the transmission zero at s radius.

/pdf/generalized-real-perturbation-values-with-applications-to-234p7m3jnd.pdf

Generalized real perturbation values with applications to the structured real controllability radius of LTI systems

Reliability of Robust Decentralized Controllers

A computational technique for finding time optimal controls of nonlinear time-varying systems

A fundamental limitation on the implementation of constrained model predictive control (MPC) is the excessive computational time required to evaluate the constrained controls at each sample interval. Prior results show that premature termination of algorithms which solve the quadratic programming (QP) subproblem associated with the computation of the MPC controller at each sampling interval, can be used to decrease the necessary CPU time, with favorable results, but there is no guarantee on the performance of such ad hoc methods. In this paper, a new supervisory algorithm is introduced in order to guarantee bounds on the performance of any non-feasible algorithm, which on solving the QP subproblem is terminated before convergence has occurred. This supervisory algorithm allows for real-time control of a large class of systems using a suboptimal constrained MPC controller with guaranteed bounds on its performance. An example is included to illustrate how this method performs under the limitations of real-time control.

Guaranteed bounds on the performance cost of a fast real-time suboptimal constrained MPC controller

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac11-proceedings/data/html/papers/0772.pdf

Edward J. Davison

Papers

Generalized real perturbation values with applications to the structured real controllability radius of LTI systems

Reliability of Robust Decentralized Controllers

A computational technique for finding time optimal controls of nonlinear time-varying systems

Guaranteed bounds on the performance cost of a fast real-time suboptimal constrained MPC controller

Optimal Servomechanism Control of Plants With Fewer Inputs Than Outputs