Invariant Ellipsoids Research Articles

Exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation

We present a necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under a saturated linear feedback. The condition is given in terms of linear matrix inequalities (LMIs) and can be easily used for optimization-based analysis and design.

On enlarging the basin of attraction for linear systems under saturated linear feedback

We consider the problem of enlarging the basin of attraction for a linear system under saturated linear feedback. An LMI-based approach to this problem is developed. For discrete-time system, this approach is enhanced by the lifting technique, which leads to further enlargement of the basin of attraction. The low convergence rate inherent with the large invariant set (hence, the large basin of attraction) is prevented by the construction of a sequence of invariant ellipsoids nested within the large one obtained.

Linear Matrix Inequalities In System And Control Theory

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.