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

In this paper we introduce a scalable computational procedure to achieve local consistency among local components in a distributed system. We show that by defining an appropriate memory set in each local component we can guarantee the termination of the proposed procedure in a relatively general distributed setup.

An algorithm to achieve local consistency in distributed systems

This paper refines an earlier localization procedure used to design optimal nonblocking distributed supervisory controllers in discrete-event systems (DES). The earlier algorithm needed a control consistency relation involving two conditions, and introduced superfluous selfloops. We propose a refined procedure, including a newly defined weak control consistency relation, and a cleanup algorithm, which results in simpler and cleaner controllers. It is proved to be correct, and illustrated by a Transfer Line plant.

On computation of distributed supervisory controllers in discrete-event systems

Time Scales Hierarchical in Stably Control Nested Systems

Recently we studied communication delay in distributed control of untimed discrete-event systems based on supervisor localization. We proposed a property called delay-robustness: the overall system behavior 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 {\it tick}. First, we propose a timed channel model and define timed delay-robustness; for the latter, a polynomial 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 channeled event. Finally, we demonstrate delay-robustness on the example of an under-load tap-changing transformer.

W. M. Wonham

Papers

An algorithm to achieve local consistency in distributed systems

On computation of distributed supervisory controllers in discrete-event systems

Time Scales Hierarchical in Stably Control Nested Systems

Delay-Robustness in Distributed Control of Timed Discrete-Event Systems Based on Supervisor Localization

Symbolic reachability analysis and maximally permissive entrance control for globally synchronized templates