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.

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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 deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output (MIMO) systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

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Controller design of multivariable LTI unknown systems

Decoupling theory and robust servomechanism theory are applied to the design of linear multivariable systems with large parameter variations. In addition to being approximately decoupled in the transient period, the over-all system achieves tracking and disturbance rejection robustly in the steady state. An example in flight control system is given.

Design of flight control systems via robust decoupled servomechanism theory

This paper deals with the position and force control of a robot manipulator in which the end-effector is required to move along a specified trajectory with a specified contact force on a plane or general surface. Such a system is modeled as a nonlinear descriptor system consisting of a set of nonlinear differential equations and algebraic equations. A method of nonlinear state feedback and state space transformation is used to globally, exactly and totally linearize the nonlinear descriptor system into a linear descriptor system in the working space of the manipulator. Based on the resultant linear descriptor system, a necessary and sufficient condition for position and force control of robot manipulator is then obtained, and a synthesis method to design a controller is given. In the special case when the contact force is required to be zero, the controller becomes considerably simpler. >

http://ieeexplore.ieee.org/iel2/3229/9195/00411458.pdf

Position tracking and force control of robotic manipulators with a descriptor system model. I. Linearization and solution for position and force control

Suppose a controlled system denoted by S old exists with the property that robust tracking and regulation occurs in each of the system's local control agents. We wish to examine the conditions under which a new subsystem and a new set of local control agents denoted by S new can be connected to S old' so that the new outputs and previous outputs are regulated, without the need for retuning the original control agents. This problem is a generalizaiton of the results obtained in [3] which deals with the case when the control agents of S new are centralized.

Edward J. Davison

Papers

Controller design of multivariable LTI unknown systems

Design of flight control systems via robust decoupled servomechanism theory

Position tracking and force control of robotic manipulators with a descriptor system model. I. Linearization and solution for position and force control

The Decentralized Control Expanding System Problem

Decentralized synthesis of the decentralized robust servomechanism problem