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

The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems

YALMIP : a toolbox for modeling and optimization in MATLAB

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

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

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...

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

If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the systemwide behavior caused by the connections. The slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model. In this way earlier linear aggregation results by Simon et al. in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations.

Weak connections, time scales, and aggregation of nonlinear systems

A dynamic, state feedback control structure is proposed. The scheme is conceived as an adaptive controller with the equilibrium in an L/sub g/V control law as the uncertain parameter, which allows the implementation of the controller for systems with unknown equilibrium. A new property of L/sub g/V controllers is given, and it is proven that this and other important properties carry on to the proposed scheme. A synchronous machine case study shows that the proposed scheme may give better results than the L/sub g/V controller from which it is derived.

A dynamic extension for L/sub g/V controllers

In this paper a method for designing control systems with random parameters and random initial state is presented. The observed signal available for feedback is a function of the state and system parameters corrupted by additive white Gaussian noise with zero mean. The proposed control consists of an open-loop term, which is the optimal control for the parameters and initial state equal to their mean values, plus a feedback correction term. The feedback correction term is a linear function of the estimated values of the deviation in initial state and system parameters from their mean values. The control tends to the optimally sensitive control when the measurement noise tends to zero, and the feedback correction tends to zero when the measurement noise tends to infinity. A numerical experiment with a simplified model for nuclear reactor control shows that in spite of fairly large measurement noise, significant improvement in performance can be achieved using the proposed control compared to open-loop control.

Design of control systems with random parameters

A boundedness conjecture is presented which states that all signals within a specified adaptive system including the output error and parameter estimates remain globally bounded for all time despite any locally unstable behavior. Results suggested by computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system. >

http://ieeexplore.ieee.org/iel2/716/5019/00194415.pdf

On a boundedness conjecture for output error adaptive algorithms

Using the theory of integral manifolds, followed by the method of averaging. sufficient conditions are given for the existence of a bounded uniformly asymptotically stable (u.a.s.) solution of the model reference adaptive control system. These conditions, which do not require any matching assumptions or knowledge of the order of the plant, provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u.a.s. property of the solution is preserved.

Petar V. Kokotovic

Papers

Weak connections, time scales, and aggregation of nonlinear systems

A dynamic extension for L/sub g/V controllers

Design of control systems with random parameters

On a boundedness conjecture for output error adaptive algorithms

Stability of Slow Adaptation for Non-SPR Systems with Disturbances