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

Forecasting with artificial neural networks: the state of the art

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Two-time-scale output feedback design for longitudinal control of airplanes

Multimodel Strategies Under Random Disturbances and Imperfect Partial Observations

We consider an example of a second order nonlinear system with large parametric uncertainties. The two parameters of the system are assumed to belong to a finite set. The goal is to guarantee (practical) convergence of the system output to a given constant reference signal. Feedback linearization-based candidate controllers with pole placement are designed for each possible set of parameters. After that, we consider the design of a high-level logic-based supervisor to organize switching between these candidate controllers. Three different approaches are used and compared.

/pdf/comparison-of-logic-based-switching-control-designs-for-a-53fjf6683i.pdf

Comparison of logic-based switching control designs for a nonlinear system

In this work, we address the tracking problem for an unknown reference comprised of two sinusoids. We propose an adaptive servocompensator based on a pair of frequency estimators. Slow adaptation is used to create three time scales within the closed-loop system, corresponding to the controller and plant dynamics, fast frequency estimate, and slow frequency estimate. Stability of the boundary-layer system, comprised of the servocompensator and plant dynamics, is achieved with a stabilizing controller. Novel nonlinear analysis is then performed on the average system to show global asymptotic stability. The algorithm's performance is verified by experiments conducted on a commercial nanopositioner, and its performance is shown to be comparable to that of iterative learning control.

/pdf/tracking-an-unknown-two-frequency-reference-using-a-35406rhxel.pdf

Tracking an unknown two-frequency reference using a frequency estimator-based servocompensator

This paper presents a high-gain feedback stabilizing control algorithm in which the high-gain parameter is adapted on line. The algorithm is developed for a class of nonlinear systems which can be viewed as the nonlinear counterpart of uniform rank multivariable linear systems. The system can be unknown except for a number of vital pieces of information. For singleinput single-output linear systems such information is usually required in the traditional adaptive control literature.

Hassan K. Khalil

Papers

Two-time-scale output feedback design for longitudinal control of airplanes

Multimodel Strategies Under Random Disturbances and Imperfect Partial Observations

Comparison of logic-based switching control designs for a nonlinear system

Tracking an unknown two-frequency reference using a frequency estimator-based servocompensator

Nonlinear systems usik h1c;hgain feedback