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

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

Technical Communique: Delay-dependent criteria for robust stability of time-varying delay systems

This paper is concerned with the controller design of networked control systems (NCS). A new model of the NCSs is provided under consideration of both the network-induced delay and the data packet dropout in the transmission. In terms of the given model, a controller design method is proposed based on a delay-dependent approach. The feedback gain of a memoryless controller and the maximum allowable value of the network-induced delay can be derived by solving a set of linear matrix inequalities. Two examples are given to show the effectiveness of our method.

State feedback controller design of networked control systems

A sufficient condition for the stability of the linear uncertain time-delay systems is presented. The result obtained can include information on the size of the delay, and therefore can be a delay-dependent stability condition. The Lyapunov method is employed to investigate the problem. The result is demonstrated by an illustrative example. >

Robust stability of delay dependence for linear uncertain systems

Based on the linear matrix inequality method, we introduce the robust stability of uncertain linear stochastic differential delay systems with delay dependence. The parameter uncertainty is norm-bounded and the delays are time varying. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems.

An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays

Robust stability of interval time-delay systems with delay-dependence

Dosimetric comparisons of helical tomotherapy and step-and-shoot intensity-modulated radiotherapy in nasopharyngeal carcinoma

The stability for cellular neural networks (CNNs) with time-varying delay is introduced by using a linear-matrix inequality. A sufficient condition related to the global asymptotic stability for delay CNNs is proposed. It is shown that the condition relies on the dependence of the delay. This condition is less restrictive than that given in the literature.

Te-Jen Su

Papers

Robust stability of delay dependence for linear uncertain systems

An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays

Robust stability of interval time-delay systems with delay-dependence

Dosimetric comparisons of helical tomotherapy and step-and-shoot intensity-modulated radiotherapy in nasopharyngeal carcinoma

Stability of cellular neural networks with time-varying delay