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)

Sufficient conditions for the one-dimensional time intercept problem are derived for two multi-input systems where the admissible control vectors belong to either hyperspheres or hypercubes.

https://ieeexplore.ieee.org/iel5/9/24111/01099376.pdf

A minimum time intercept problem

In this paper, we consider linear time invariant (LTI) systems with parameter uncertainty. For such systems, we present global optimization techniques to determine permissible perturbations of the parameters of the system that maintain stability (the so-called parameter stability margins), for cases in which the coefficients of the characteristic equation of the system are polynomial functions of the uncertain parameters. The parameter uncertainty domains for maintaining stability are characterized as hypersolids, defined with respect to lp -norms for various values of p ∊ (1, ∞). Algorithms are devised based on the reformulation–linearization/convexification technique (RLT) in concert with branch-and-bound methods to solve the underlying parametric non-convex subproblems for computing the stability margins. Several illustrative examples are solved to demonstrate the efficacy of the proposed approach towards producing global optimal solutions. We also present comparative computational experience with the ...

Computation of parameter stability margins using polynomial programming techniques

In traditional web handling processes, web tension and speed are typically controlled assuming that the web system consists of a number of single input and single output systems. This assumption often results in large interactions occurring in the closed loop system between the control loops, and hence results in high quality control being difficult to achieve. In this paper, the control of the web handling processes is treated as a multivariable servomechanism problem. Two types of controller design, the "perfect control servomechanism controller" and the "tuning regulator", are studied and implemented on an industrial web machine. The experimental results obtained show that these controllers provide excellent tension and speed response.

Servomechanism controller design of web handling systems

A general description of the decentralized control problem, with particular emphasis on large scale systems, is made. In this problem, constraints on the structure of the information flow between the manipulated inputs of the system and measured outputs of the system are imposed. Typically, it is desired to find a controller for this system (subject to the above constraints), so that stability of the resultant closed loop system is obtained, and so that regulation/tracking of the outputs of the system occurs, independent of any input disturbances occurring in the system. A motivation for dealing with the decentralized problem is made, classical ways of solving the problem are described, and recent results obtained on the problem are surveyed. Some numerical examples are included, in particular, a power system consisting of three interconnected synchronous machines; it is shown in this power system that there is no real advantage is using a (more complex) centralized control system over the conventional (and more simple) decentralized control system which is normally applied.

Decentralized control in large multivariable systems

This paper deals with the characterization of infinite transmission zeros of linear, time-invariant state-space systems. For a square system (equal number of inputs and outputs), the number of infinite transmission zeros is given by the difference between the number of poles and the number of finite zeros. However, for systems with an unequal number of inputs and outputs, such a relationship does not hold. In this work, it is shown that the number of infinite transmission zeros is equal to the number of poles minus the maximum number of transmission zeros of the largest square subsystem. An algorithm is also provided to determine the number of infinite transmission zeros computationally. >

Edward J. Davison

Papers

A minimum time intercept problem

Computation of parameter stability margins using polynomial programming techniques

Servomechanism controller design of web handling systems

Decentralized control in large multivariable systems

Characterization of infinite transmission zeros of state space systems