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

In an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed-loop system even when the neglected modes are asymptotically stable. The purpose of this note is to show that this instability phenomenon might take place even when the reduced-order design model is strictly proper.

A further note on the robustness of output feedback control methods to modeling errors

This paper discusses linear-quadratic Nash games for systems with slow and fast modes. Singular perturbation is employed to replace a Nash game played on the full model by a game played on a reduced order model. The well-posedness of different solutions corresponding to different state feedback information structures is considered. An important relation between the feedback information structure and the well-posedness of the game is found and used to conjecture special cases when the linear memoryless closed-loop solution is well-posed.

Feedback and well-posedness of singularly perturbed Nash games

Logic-based switching for robust control of minimum-phase nonlinear systems

Layered neural networks are used in nonlinear adaptive control problems. Both the discrete-time case and the continuous-time case are considered. For the discrete-time case, the plant is an unknown SISO feedback-linearizable discrete-time system with general relative degree, represented by an input-output model; a state space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable. A layered neural network is used to model the unknown system and generate the feedback control. Based on the error between the plant output and the model output, the weights of the neural network are updated. For the continuous-time case, we work on a SISO relative-degree-one system with zero dynamics, and on a MIMO general relative degree system without zero dynamics. The neural network is used to model the nonlinear functions of the continuous-time systems, instead of modeling the whole system as in the discrete-time case; and the control law for the continuous-time case does not involve an explicit system identification process, as appears in the discrete-time case. The convergence results obtained for both cases are regional in state space, yet local in parameter space.

Hassan K. Khalil

Papers

A further note on the robustness of output feedback control methods to modeling errors

Feedback and well-posedness of singularly perturbed Nash games

Logic-based switching for robust control of minimum-phase nonlinear systems

Adaptive control of a class of nonlinear systems using neural networks

Output feedback performance recovery in the presence of uncertainties