By Eli Gershon

Complex issues up to the mark and Estimation of State-Multiplicative Noisy platforms starts with an advent and wide literature survey. The textual content proceeds to hide the sector of H∞ time-delay linear structures the place the problems of balance and L2−gain are awarded and solved for nominal and unsure stochastic platforms, through the input-output technique. It provides suggestions to the issues of state-feedback, filtering, and measurement-feedback keep watch over for those platforms, for either the continual- and the discrete-time settings. within the continuous-time area, the issues of reduced-order and preview monitoring keep an eye on also are provided and solved. the second one a part of the monograph matters non-linear stochastic country- multiplicative platforms and covers the problems of balance, regulate and estimation of the platforms within the H∞ experience, for either continuous-time and discrete-time instances. The publication additionally describes distinctive themes corresponding to stochastic switched platforms with reside time and peak-to-peak filtering of nonlinear stochastic platforms. The reader is brought to 6 useful engineering- orientated examples of noisy state-multiplicative regulate and filtering difficulties for linear and nonlinear structures. The booklet is rounded out through a three-part appendix containing stochastic instruments invaluable for a formal appreciation of the textual content: a uncomplicated creation to stochastic regulate strategies, facets of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback regulate difficulties of stochastic switched structures with dwell-time. complicated themes up to speed and Estimation of State-Multiplicative Noisy structures can be of curiosity to engineers engaged up to speed structures study and improvement, to graduate scholars focusing on stochastic keep an eye on thought, and to utilized mathematicians attracted to regulate difficulties. The reader is predicted to have a few acquaintance with stochastic keep watch over concept and state-space-based optimum regulate concept and techniques for linear and nonlinear systems.

Table of Contents

Cover

Advanced subject matters up to the mark and Estimation of State-Multiplicative Noisy Systems

ISBN 9781447150695 ISBN 9781447150701

Preface

Contents

1 Introduction

1.1 Stochastic State-Multiplicative Time hold up Systems

1.2 The Input-Output technique for not on time Systems

1.2.1 Continuous-Time Case

1.2.2 Discrete-Time Case

1.3 Non Linear keep an eye on of Stochastic State-Multiplicative Systems

1.3.1 The Continuous-Time Case

1.3.2 Stability

1.3.3 Dissipative Stochastic Systems

1.3.4 The Discrete-Time-Time Case

1.3.5 Stability

1.3.6 Dissipative Discrete-Time Nonlinear Stochastic Systems

1.4 Stochastic approaches - brief Survey

1.5 suggest sq. Calculus

1.6 White Noise Sequences and Wiener Process

1.6.1 Wiener Process

1.6.2 White Noise Sequences

1.7 Stochastic Differential Equations

1.8 Ito Lemma

1.9 Nomenclature

1.10 Abbreviations

2 Time hold up structures - H-infinity keep an eye on and General-Type Filtering

2.1 Introduction

2.2 challenge formula and Preliminaries

2.2.1 The Nominal Case

2.2.2 The powerful Case - Norm-Bounded doubtful Systems

2.2.3 The strong Case - Polytopic doubtful Systems

2.3 balance Criterion

2.3.1 The Nominal Case - Stability

2.3.2 powerful balance - The Norm-Bounded Case

2.3.3 strong balance - The Polytopic Case

2.4 Bounded actual Lemma

2.4.1 BRL for behind schedule State-Multiplicative platforms - The Norm-Bounded Case

2.4.2 BRL - The Polytopic Case

2.5 Stochastic State-Feedback Control

2.5.1 State-Feedback keep watch over - The Nominal Case

2.5.2 powerful State-Feedback keep watch over - The Norm-Bounded Case

2.5.3 powerful Polytopic State-Feedback Control

2.5.4 instance - State-Feedback Control

2.6 Stochastic Filtering for not on time Systems

2.6.1 Stochastic Filtering - The Nominal Case

2.6.2 powerful Filtering - The Norm-Bounded Case

2.6.3 powerful Polytopic Stochastic Filtering

2.6.4 instance - Filtering

2.7 Stochastic Output-Feedback keep an eye on for not on time Systems

2.7.1 Stochastic Output-Feedback regulate - The Nominal Case

2.7.2 instance - Output-Feedback Control

2.7.3 powerful Stochastic Output-Feedback keep an eye on - The Norm-Bounded Case

2.7.4 powerful Polytopic Stochastic Output-Feedback Control

2.8 Static Output-Feedback Control

2.9 powerful Polytopic Static Output-Feedback Control

2.10 Conclusions

3 Reduced-Order H-infinity Output-Feedback Control

3.1 Introduction

3.2 challenge Formulation

3.3 The not on time Stochastic Reduced-Order H keep an eye on 8

3.4 Conclusions

4 monitoring keep an eye on with Preview

4.1 Introduction

4.2 challenge Formulation

4.3 balance of the not on time monitoring System

4.4 The State-Feedback Tracking

4.5 Example

4.6 Conclusions

4.7 Appendix

5 H-infinity regulate and Estimation of Retarded Linear Discrete-Time Systems

5.1 Introduction

5.2 challenge Formulation

5.3 Mean-Square Exponential Stability

5.3.1 instance - Stability

5.4 The Bounded genuine Lemma

5.4.1 instance - BRL

5.5 State-Feedback Control

5.5.1 instance - powerful State-Feedback

5.6 behind schedule Filtering

5.6.1 instance - Filtering

5.7 Conclusions

6 H-infinity-Like regulate for Nonlinear Stochastic Syste8 ms

6.1 Introduction

6.2 Stochastic H-infinity SF Control

6.3 The In.nite-Time Horizon Case: A Stabilizing Controller

6.3.1 Example

6.4 Norm-Bounded Uncertainty within the desk bound Case

6.4.1 Example

6.5 Conclusions

7 Non Linear platforms - H-infinity-Type Estimation

7.1 Introduction

7.2 Stochastic H-infinity Estimation

7.2.1 Stability

7.3 Norm-Bounded Uncertainty

7.3.1 Example

7.4 Conclusions

8 Non Linear structures - dimension Output-Feedback Control

8.1 advent and challenge Formulation

8.2 Stochastic H-infinity OF Control

8.2.1 Example

8.2.2 The Case of Nonzero G2

8.3 Norm-Bounded Uncertainty

8.4 In.nite-Time Horizon Case: A Stabilizing H Controller 8

8.5 Conclusions

9 l2-Gain and powerful SF keep an eye on of Discrete-Time NL Stochastic Systems

9.1 Introduction

9.2 Su.cient stipulations for l2-Gain= .:ASpecial Case

9.3 Norm-Bounded Uncertainty

9.4 Conclusions

10 H-infinity Output-Feedback keep watch over of Discrete-Time Systems

10.1 Su.cient stipulations for l2-Gain= .:ASpecial Case

10.1.1 Example

10.2 The OF Case

10.2.1 Example

10.3 Conclusions

11 H-infinity keep an eye on of Stochastic Switched structures with live Time

11.1 Introduction

11.2 challenge Formulation

11.3 Stochastic Stability

11.4 Stochastic L2-Gain

11.5 H-infinity State-Feedback Control

11.6 instance - Stochastic L2-Gain Bound

11.7 Conclusions

12 powerful L-infinity-Induced regulate and Filtering

12.1 Introduction

12.2 challenge formula and Preliminaries

12.3 balance and P2P Norm certain of Multiplicative Noisy Systems

12.4 P2P State-Feedback Control

12.5 P2P Filtering

12.6 Conclusions

13 Applications

13.1 Reduced-Order Control

13.2 Terrain Following Control

13.3 State-Feedback keep an eye on of Switched Systems

13.4 Non Linear platforms: dimension Output-Feedback Control

13.5 Discrete-Time Non Linear platforms: l2-Gain

13.6 L-infinity keep watch over and Estimation

A Appendix: Stochastic keep an eye on tactics - simple Concepts

B The LMI Optimization Method

C Stochastic Switching with reside Time - Matlab Scripts

References

Index

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**Sample text**

Following the latter derivation, we obtain solutions to the problems of: state-feedback control, general-type ﬁltering, and full-order measurement control for nominal systems and for uncertain ones. The latter solutions are followed by the solution to the SOF control problem. The latter problem is also solved later, in Chapter 3, as a special case of the reduced-order control problem. Various examples are given that demonstrate the applicability of the theory involved. E. Gershon & U. Shaked: Advanced Topics in Control & Estimation, LNCIS 439, pp.

Fk )k∈N an increasing family of σ−algebras Fk ⊂ F . ˜l2 ([0, N ]; Rn ) the space of nonanticipative stochastic processes. {fk }={fk }k∈[0,N ] in Rn with respect to (Fk )k∈[0,N ) satisfying N N ||fk ||˜2l = E{ 0 ||fk ||2 } = 0 E{||fk ||2 } < ∞ 2 l2 ([0, ∞); Rn ). , fk ∈ ˜ ˜l2 ([0, ∞); Rn ) the above space for N → ∞ ˜ 2 ([0, T ); Rk ) the space of non anticipative stochastic processes. L f (·) = (f (t))t∈[0,T ] in Rk with respect to (Ft )t∈[0,T ) satisfying T T ||f (·)||2L˜ = E{ 0 ||f (t)||2 dt} = 0 E{||f (t)||2 }dt < ∞.

N }. the trace of a matrix. the Kronecker delta function. the Dirac delta function. the set of natural numbers. the sample space. σ−algebra of subsets of Ω called events. the probability measure on F . probability of (·). the space of square-summable Rn − valued functions. 10 Abbreviations 19 on the probability space (Ω, F , P). (Fk )k∈N an increasing family of σ−algebras Fk ⊂ F . ˜l2 ([0, N ]; Rn ) the space of nonanticipative stochastic processes. {fk }={fk }k∈[0,N ] in Rn with respect to (Fk )k∈[0,N ) satisfying N N ||fk ||˜2l = E{ 0 ||fk ||2 } = 0 E{||fk ||2 } < ∞ 2 l2 ([0, ∞); Rn ).