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 this paper, we present an output feedback regulator for nonlinear systems that could potentially include unstable zero dynamics. The regulation scheme adopted herein incorporates continuously-implemented sliding mode control and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. The result is illustrated using a simulation.

Output regulation of non-minimum phase nonlinear systems using an extended high-gain observer

A new test for D-stability

In this paper we propose a new method for the design of an output feedback controller for a minimum-phase, uncertain, input-nonaffine, nonlinear system. By combining dynamic inversion control together with extended high-gain observer, our output feedback controller is able to bring the trajectories of the closed-loop system arbitrarily close to that of a given target system. Stability analysis of the closed-loop system is presented along with simulation results of trajectory tracking.

Performance recovery under output feedback for input nonaffine nonlinear systems

A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables. >

A real Schur form method for modeling singularly perturbed systems

This paper studies the output regulation problem for linear systems subject to input constraints It presents a new controller that uses a conditional servocompensator Previous work introduced the conditional servocompensator, which acts as a traditional servocompensator only in a neighborhood of the zero-error manifold, while acting as a stable system outside a boundary layer, leading to improvement in the transient response while achieving zero steady-state regulation error Starting with a low-gain stabilizing state feedback controller, based on the solution of an algebraic Riccati equation, Lyapunov redesign is used to implement the state feedback control in a saturated high-gain feedback form that includes the conditional servocompensator The design is extended to output feedback via a full-order high-gain observer

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Hassan K. Khalil

Papers

Output regulation of non-minimum phase nonlinear systems using an extended high-gain observer

A new test for D-stability

Performance recovery under output feedback for input nonaffine nonlinear systems

A real Schur form method for modeling singularly perturbed systems

Output regulation of linear systems subject to input constraints