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

This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

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Supervisory control of a class of discrete event processes

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Mathematical Control Theory: Deterministic Finite Dimensional Systems

A long-run equilibrium theory of turnover is presented and is shown to explain the important regularities that have been observed by empirical investigators. A worker's productivity in a particular job is not known ex ante and becomes known more precisely as the worker's job tenure increases. Turnover is generated by the existence of a nondegenerate distribution of the worker's productivity across different. The nondegeneracy is caused by the assumed variation in the quality of the worker-employer match.

Job Matching and the Theory of Turnover

A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

The control of discrete event systems

A model of component consistency in distributed diagnosis

Recently, we studied communication delay in distributed control of untimed discrete-event systems based on supervisor localisation. We proposed a property called delay-robustness: the overall system behaviour controlled by distributed controllers with communication delay is logically equivalent to its delay-free counterpart. In this paper, we extend our previous work to timed discrete-event systems, in which communication delays are counted by a special clock event tick. First, we propose a timed channel model and define timed delay-robustness; for the latter, a verification procedure is presented. Next, if the delay-robust property does not hold, we introduce bounded delay-robustness, and present an algorithm to compute the maximal delay bound (measured by number of ticks) for transmitting a channelled event. Finally, we demonstrate delay-robustness on the example of an under-load tap-changing transformer.

Delay-robustness in distributed control of timed discrete-event systems based on supervisor localisation

On computation of supremal controllable, normal sublanguages

In parallel and/or distributed architectures, strict concurrency (simultaneity of events) may have critical implications for the validity of a proposed supervisory control law. The authors consider this problem in the Ramadge-Wonham framework of controlled automata. They derive a simpler description of the concept of weak interaction introduced in earlier work, together with new necessary and sufficient conditions for state-feedback control to remain valid in the presence of strict concurrency. >

Concurrency and state feedback in discrete-event systems

An extremum control system is considered in which the output from a plant is minimized by adjusting inputs to the plant in discrete steps of constant size. The direction of stepping is determined by estimates of the true output in the presence of Gaussian noise. The criterion of steady-state performance is the average deviation of the true output from the minimum. Performance of a system with single-input plant is computed when one estimate of output is made after each step; the analysis is supported by experimental results. Analysis is simpler when two independent estimates are made per step; performances of the two types of system are compared. Limiting results for vanishing step size in the two-estimate system are derived for a single-input plant with both output noise and input disturbance, and for a multi-input plant with output noise only.

W. M. Wonham

Papers

A model of component consistency in distributed diagnosis

Delay-robustness in distributed control of timed discrete-event systems based on supervisor localisation

On computation of supremal controllable, normal sublanguages

Concurrency and state feedback in discrete-event systems

Extremum Control in the Presence of Noise