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...

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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

We investigate the possibility of having an input-output model that has a specific structure for multivariable input-output linearizable systems.

Input-output models for a class of nonlinear systems

Disturbance isolation via high gain feedback.

This paper deals with designing an output feedback control for a class of single-input, single-output nonlinear systems that are represented by input-output models. The authors augment a series of m integrators at the input side, where m is the highest derivative of the input, and redefine the output and its derivatives to obtain an (n+m)-dimensional state model, where n is the order of the system. The purpose of the design is to force the output to asymptotically track a time-varying reference signal, while rejecting a time-varying disturbance input. The authors assume that exogenous signals are generated by a linear exosystem. Also the authors assume that the nonlinearities of the system will introduce only a finite number of harmonics of the original modes. This will enable one to identify the internal model as a linear servo-compensator. After augmenting the original system with the servo-compensator, the authors present conditions that will characterize a state feedback stabilizing control. Then, using a high gain observer, the authors show that the asymptotic properties achieved under state feedback control can be recovered. >

http://ieeexplore.ieee.org/iel2/3229/9194/00411190.pdf

Robust tracking for nonlinear systems represented by input-output models

In this paper, we consider the frequency synchronization problem in a network of lossless, connected and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm that achieves practical frequency synchronization in the presence of unknown time-varying power demand. It is shown that the synchronization error can be made arbitrarily small by tuning a controller parameter. Finally, simulations are performed to show the efficacy of the proposed controller.

Practical Frequency Synchronization in Power Systems Using Extended High-Gain Observer Under Unknown Time-Varying Power Demand

The paper is concerned with the design of an integral control for minimum-phase nonlinear systems that have a well-defined relative degree. Earlier work by the author and coworkers has shown how integral control can be combined with robust control techniques to achieve nonlocal and semiglobal regulation results. The results are applicable to output feedback control problems through the use of high-gain observers and saturation nonlinearities. When used with sliding-mode control, the technique produces universal integral regulators that have been shown to coincide with PI and PID controllers, followed by limiters, for relative-degree-one systems and relative-degree-two systems. The use of integral action improves the steady-state response at the expense of degrading the transient response. The present paper summarizes two recent techniques to modify the universal integral regulator so as to improve its transient performance. One technique uses antiwindup integration, while the other uses nonlinear integrators.

Hassan K. Khalil

Papers

Input-output models for a class of nonlinear systems

Disturbance isolation via high gain feedback.

Robust tracking for nonlinear systems represented by input-output models

Practical Frequency Synchronization in Power Systems Using Extended High-Gain Observer Under Unknown Time-Varying Power Demand

Improved Performance of Universal Integral Regulators