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

Deals with the design of robust integral control for single-input single-output (SISO) nonlinear systems with well defined normal form and exponentially stable zero dynamics. We develop further the universal controller design that was initiated in the work of Khalil (2000). The modification to the controller of Khalil is done in two steps. First, the integrator equation is modified to include not only the tracking error, but a linear combination of the tracking error and its derivatives, up to a certain order. Next, an additional input, in the spirit of classical anti-reset windup is added to the integrator to prevent it from winding up. Analytical results are given for both regional as well as,semiglobal regulation. The performance of the proposed controller is illustrated through simulations.

http://ieeexplore.ieee.org/iel5/7709/21129/00980843.pdf

Universal integral controllers with anti-reset windup for minimum phase nonlinear systems

In this paper, feedback linearization is used to control the speed of a surface mount Permanent Magnet Synchronous Motor (PMSM). An extended high-gain observer is also used to estimate both the speed of the motor and the disturbance present in the system to recover the performance of feedback linearization. The disturbance is assumed to be unknown, and time-varying but bounded. Stability of the output feedback system is shown. Finally, simulation and experimental results confirm stability, robustness, and performance of the system.

Speed control of Permanent Magnet Synchronous Motor using extended high-gain observer

An implicit singularly perturbed system \dot{x} = A(\epsilon)x , where A(0) is singular, is considered. This note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales. The decomposed form of the system is used to construct a uniform asymptotic approximation to \exp (A(\epsilon)t) .

Time scale decomposition of linear implicit singularly perturbed systems

A technique for the longitudinal control of a platoon of automated vehicles is presented. A nonlinear model is used to represent the vehicle dynamics of each vehicle within the platoon. The controlled vehicle is assumed to be capable of measuring (or estimating) necessary dynamical information from the vehicle immediately in front of it by its on-board sensors. The computer in the vehicle processes the measured data and generates proper throttling and braking actions to follow the vehicle in front at a safe distance. Simulations are presented for the case of a platoon of four cars following a leader.

Hassan K. Khalil

Papers

Universal integral controllers with anti-reset windup for minimum phase nonlinear systems

Speed control of Permanent Magnet Synchronous Motor using extended high-gain observer

Time scale decomposition of linear implicit singularly perturbed systems

Longitudinal adaptive control of a platoon of vehicles

Decentralized stabilization of systems with slow and fast modes