Author

# Petar V. Kokotovic

Other affiliations: Washington State University, University of Illinois at Urbana–Champaign, University of California

Bio: Petar V. Kokotovic is an academic researcher from University of California, Santa Barbara. The author has contributed to research in topic(s): Nonlinear system & Adaptive control. The author has an hindex of 83, co-authored 354 publication(s) receiving 40395 citation(s). Previous affiliations of Petar V. Kokotovic include Washington State University & University of Illinois at Urbana–Champaign.

##### Papers published on a yearly basis

##### Papers

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01 Jan 1995

TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.

Abstract: From the Publisher:
Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.

6,912 citations

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01 Jan 1986

TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.

Abstract: From the Publisher:
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.
Audience
Control engineers and graduate students who seek an introduction to singular perturbation methods in control will find this text useful. The book also provides research workers with sketches of problems in the areas of robust, adaptive, stochastic, and nonlinear control. No previous knowledge of singular perturbation techniques is assumed.
About the Authors
Petar Kokotovic is Director of the Center for Control Engineering and Computation at the University of California, Santa Barbara. Hassan K. Khalil is Professor of Electrical and Computer Engineering at Michigan State University. John O'Reilly is Professor of Electronics and Electrical Engineering at the University of Glasgow, Scotland.

2,328 citations

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TL;DR: In this article, the authors introduce the concept of passive design tools as a design tool for adaptive control and propose a cascade design with feedback passivation of Cascades and partial-state feedback.

Abstract: 1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation -- 2 Passivity Concepts as Design Tools -- 2.1 Dissipativity and Passivity -- 2.2 Interconnections of Passive Systems -- 2.3 Lyapunov Stability and Passivity -- 2.4 Feedback Passivity -- 2.5 Summary -- 2.6 Notes and References -- 3 Stability Margins and Optimality -- 3.1 Stability Margins for Linear Systems -- 3.2 Input Uncertainties -- 3.3 Optimality, Stability, and Passivity -- 3.4 Stability Margins of Optimal Systems -- 3.5 Inverse Optimal Design -- 3.6 Summary -- 3.7 Notes and References -- 4 Cascade Designs -- 4.1 Cascade Systems -- 4.2 Partial-State Feedback Designs -- 4.3 Feedback Passivation of Cascades -- 4.4 Designs for the TORA System -- 4.5 Output Peaking: an Obstacle to Global Stabilization -- 4.6 Summary -- 4.7 Notes and References -- 5 Construction of Lyapunov functions -- 5.1 Composite Lyapunov functions for cascade systems -- 5.2 Lyapunov Construction with a Cross-Term -- 5.3 Relaxed Constructions -- 5.4 Stabilization of Augmented Cascades -- 5.5 Lyapunov functions for adaptive control -- 5.6 Summary -- 5.7 Notes and references -- 6 Recursive designs -- 6.1 Backstepping -- 6.2 Forwarding -- 6.3 Interlaced Systems -- 6.4 Summary and Perspectives -- 6.5 Notes and References -- A Basic geometric concepts -- A.1 Relative Degree -- A.2 Normal Form -- A.3 The Zero Dynamics -- A.4 Right-Invertibility -- A.5 Geometric properties -- B Proofs of Theorems 3.18 and 4.35 -- B.1 Proof of Theorem 3.18 -- B.2 Proof of Theorem 4.35.

1,779 citations

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TL;DR: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed, which substantially enlarges the class of non linear systems with unknown parameters for which global stabilization can be achieved.

Abstract: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed. The coordinate-free geometric conditions, which characterize this class of systems, do not constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called parametric-pure feedback form. When this form is strict, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results use simple analytical tools, familiar to most control engineers. >

1,612 citations

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TL;DR: In this paper, a systematic procedure is developed for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems, which are transformable into the so-called pure-feedback form.

Abstract: A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions, which characterize this class of systems, neither restrict the location of the unknown parameters, nor constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called pure-feedback form. When this form is "strict", the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results of this paper use simple analytical tools, familiar to most control engineers.

1,494 citations

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01 Jan 1994

TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.

Abstract: 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.

10,744 citations

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02 Sep 2004

TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.

Abstract: 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

7,174 citations

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TL;DR: In this article, the authors present a model for dynamic control systems based on Adaptive Control System Design Steps (ACDS) with Adaptive Observers and Parameter Identifiers.

Abstract: 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.

4,375 citations

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26 Jun 2003

TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index

Abstract: 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

3,858 citations

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TL;DR: A tutorial account of variable structure control with sliding mode is presented, introducing in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach.

Abstract: A tutorial account of variable structure control with sliding mode is presented. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. >

2,769 citations