By Eli Gershon

Complicated subject matters up to speed and Estimation of State-Multiplicative Noisy platforms starts off with an creation and broad literature survey. The textual content proceeds to hide the sphere of H∞ time-delay linear structures the place the problems of balance and L2−gain are provided and solved for nominal and unsure stochastic structures, through the input-output process. It provides recommendations 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 regulate also are awarded and solved. the second one a part of the monograph matters non-linear stochastic nation- multiplicative platforms and covers the problems of balance, keep an eye on and estimation of the structures within the H∞ experience, for either continuous-time and discrete-time circumstances. The publication additionally describes designated subject matters 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 keep watch over and filtering difficulties for linear and nonlinear platforms. The publication is rounded out through a three-part appendix containing stochastic instruments helpful for a formal appreciation of the textual content: a easy advent to stochastic keep watch over tactics, elements 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 subject matters up to speed and Estimation of State-Multiplicative Noisy structures could be of curiosity to engineers engaged on top of things platforms examine and improvement, to graduate scholars focusing on stochastic keep an eye on concept, and to utilized mathematicians drawn to regulate difficulties. The reader is anticipated to have a few acquaintance with stochastic keep watch over concept and state-space-based optimum keep an eye on idea and techniques for linear and nonlinear systems.

Table of Contents

Cover

Advanced subject matters up to speed 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 process 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 tactics - 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 watch over and General-Type Filtering

2.1 Introduction

2.2 challenge formula and Preliminaries

2.2.1 The Nominal Case

2.2.2 The strong Case - Norm-Bounded doubtful Systems

2.2.3 The powerful Case - Polytopic doubtful Systems

2.3 balance Criterion

2.3.1 The Nominal Case - Stability

2.3.2 strong balance - The Norm-Bounded Case

2.3.3 strong balance - The Polytopic Case

2.4 Bounded actual Lemma

2.4.1 BRL for not on time 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 regulate - The Nominal Case

2.5.2 powerful State-Feedback regulate - The Norm-Bounded Case

2.5.3 strong Polytopic State-Feedback Control

2.5.4 instance - State-Feedback Control

2.6 Stochastic Filtering for behind schedule Systems

2.6.1 Stochastic Filtering - The Nominal Case

2.6.2 powerful Filtering - The Norm-Bounded Case

2.6.3 strong 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 keep watch over - The Nominal Case

2.7.2 instance - Output-Feedback Control

2.7.3 powerful Stochastic Output-Feedback regulate - The Norm-Bounded Case

2.7.4 strong 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 watch over 8

3.4 Conclusions

4 monitoring regulate with Preview

4.1 Introduction

4.2 challenge Formulation

4.3 balance of the behind schedule monitoring System

4.4 The State-Feedback Tracking

4.5 Example

4.6 Conclusions

4.7 Appendix

5 H-infinity keep watch over 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 not on time 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 structures - 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 creation 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 regulate 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 platforms with stay 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 strong 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: size Output-Feedback Control

13.5 Discrete-Time Non Linear platforms: l2-Gain

13.6 L-infinity regulate and Estimation

A Appendix: Stochastic regulate techniques - uncomplicated Concepts

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts

References

Index

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**Additional info for Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems**

**Sample text**

40) 38 2 Time Delay Systems – H∞ Control and General-Type Filtering where A˜0 = A0 0 ˜= , B Bc C2 Ac ˜= G B1 0 , A˜1 = 0 Bc D21 G0 , F˜ = 0 0 A1 0 ˜ = , H 0 0 H0 , 0 0 0 0 , C˜ = [C1 − Cc ]. 42) ⎢ ⎥ < 0, ⎢ ∗ ⎥ 0 0 0 ∗ ∗ ∗ ∗ −I ⎢ ⎥ r ⎢ ⎥ ⎢ ∗ ⎥ ∗ ∗ ∗ ∗ ∗ −Q 0 0 ⎢ ⎥ ⎢ ∗ ∗ ∗ ∗ ∗ ∗ ∗ −Q 0 ⎥ ⎣ ⎦ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ −Q where Υ11 = Q(A˜0 + m) + (A˜0 + m)T Q + Υ12 = Q(A˜1 − m), 1 1−d R1 , Υ15 = hA˜T0 R2 + hmT R2 , Υ18 = F˜ T Q, Υ25 = hA˜T1 R2 − hmT R2 , ˜ T Q. 42) by Jˆ = diag{QJ, right and by JˆT , from the left.

5 T = Ψˆ11,i + C i 1 C i 1 , = QAi1 − Qm , T = −R1 + H i QH i , T = h f (Ai0 Q + QTm ), T = h f (Ai1 Q − QTm ). 32) that stabilizes the system and achieves a prescribed level of attenuation. 32), where A0 is replaced by A0 + B2 K, C1 is replaced by C1 + D12 K and where we assume, for simplicity, that α ¯ = 0. 5 Stochastic State-Feedback Control ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Υ11 QA1 − Qm Qm 33 QB1 Υ15 Ψ˜25 Υ16 GT Q 0 0 0 ∗ −R1 + H T QH 0 T 0 ∗ ∗ − f Q 0 −h f Qm 0 0 ∗ ∗ ∗ −γ 2 Iq h f B1T Q 0 0 0 ∗ ∗ ∗ ∗ − fQ ∗ ∗ ∗ ∗ ∗ −Ir 0 ∗ ∗ ∗ ∗ ∗ ∗ −Q ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ < 0, ⎥ ⎥ ⎥ ⎥ ⎦ where Υ11 = QB2 K + K T B2T Q + QA0 + Qm + A0 T Q + QTm + 1 1−d R1 , Υ15 = h f ([A0 + B2 K]T Q + QTm ), Υ16 = (C1 + D12 K)T , Ψ˜25 = h f (A1 T Q − QTm ).

1 Stochastic Filtering – The Nominal Case In this section we address the ﬁltering problem of the delayed state-multiplicative noisy system. 4). 40) 38 2 Time Delay Systems – H∞ Control and General-Type Filtering where A˜0 = A0 0 ˜= , B Bc C2 Ac ˜= G B1 0 , A˜1 = 0 Bc D21 G0 , F˜ = 0 0 A1 0 ˜ = , H 0 0 H0 , 0 0 0 0 , C˜ = [C1 − Cc ]. 42) ⎢ ⎥ < 0, ⎢ ∗ ⎥ 0 0 0 ∗ ∗ ∗ ∗ −I ⎢ ⎥ r ⎢ ⎥ ⎢ ∗ ⎥ ∗ ∗ ∗ ∗ ∗ −Q 0 0 ⎢ ⎥ ⎢ ∗ ∗ ∗ ∗ ∗ ∗ ∗ −Q 0 ⎥ ⎣ ⎦ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ −Q where Υ11 = Q(A˜0 + m) + (A˜0 + m)T Q + Υ12 = Q(A˜1 − m), 1 1−d R1 , Υ15 = hA˜T0 R2 + hmT R2 , Υ18 = F˜ T Q, Υ25 = hA˜T1 R2 − hmT R2 , ˜ T Q.