Hassan K. Khalil

Bio: Hassan K. Khalil is an academic researcher from Michigan State University. The author has contributed to research in topics: Nonlinear system & Nonlinear control. The author has an hindex of 57, co-authored 284 publications receiving 15992 citations. Previous affiliations of Hassan K. Khalil include Ford Motor Company & National Chiao Tung University.

Robustness of high-gain-observer-based controllers to time delays

Abstract: It is shown that a nonlinear output feedback stabilizing controller, which combines a globally bounded state feedback controller with a high-gain observer, is robust with respect to input and output time-delays in the plant. The time delay needs to be sufficiently small, but the upper bound on the delay is independent of how fast the observer is.

Reduced-order modeling of nonlinear singularly perturbed systems driven by wide-band noise

Abstract: A class of nonlinear singularly perturbed systems driven by wide-band noise is considered. The asymptotic behavior of the slow variables is studied When the fast variables are sufficiently fast (represented by µ ? 0) and the wide-band noise is sufficiently wide (represented by ϵ /spl arrow/ 0). A reduced-order Markov model to represent the behavior of the slow variables is derived. It is shown that the slow variables converge weakly to the solution of this reduced-order model as ϵ and µ tend to zero. The coefficients of this reduced-order model depend, in general, on the ratio ϵ/µ. Special cases where the model is independent of ϵ/µ are explored.

Performance of an optimal receiver in the presence of alpha-stable and Gaussian noises

Abstract: This paper deals with the optimal (in the maximum likelihood sense) detection performance of binary transmission in a mixture of a Gaussian noise and an impulsive interference modeled as an alpha-stable process. The main contribution is in the Monte Carlo simulation that shows that the Gaussianity assumption for the test statistic as reported in earlier works is not valid unless a very large number of repetitions is used.

Swing-up of the inertia wheel pendulum using impulsive torques

Abstract: The swing-up control problem of the inertia wheel pendulum is revisited in this paper. As different from existing methods, purely impulsive control inputs are used for swing-up. A mathematical formulation of the problem indicates that swing-up can be achieved using impulsive inputs applied at two discrete time instants. Two different swing-up schemes are presented and validated using numerical simulations where the impulsive inputs are approximated by high-gain feedback. The results of numerical simulations establish a direct link between high wheel velocities during swing-up and control strategies that take the pendulum directly to the upright configuration. They also indicate that the time required for swing-up is much less than that reported in the literature.

Universal regulators for minimum phase nonlinear systems

Abstract: We consider a single-input single-output (SISO) nonlinear system which has a well defined normal form with asymptotically stable zero dynamics. Using only knowledge of the relative degree and the sign of the high-frequency gain, we design an output feedback integral controller which asymptotically regulates the output to a bounded time-varying reference signal with a constant limit. We give regional as well as semi-global results.

I and i

Abstract: 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 …

Linear Matrix Inequalities in System and Control Theory

Abstract: 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.

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

Abstract: 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...