By Eli Gershon

Complicated themes on top of things and Estimation of State-Multiplicative Noisy platforms starts off with an creation and broad literature survey. The textual content proceeds to hide the sector of H∞ time-delay linear platforms the place the problems of balance and L2−gain are offered and solved for nominal and unsure stochastic structures, through the input-output method. It provides suggestions to the issues of state-feedback, filtering, and measurement-feedback keep an eye on for those structures, 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 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 watch over and estimation of the platforms within the H∞ experience, for either continuous-time and discrete-time situations. The booklet additionally describes particular subject matters akin to stochastic switched structures with live time and peak-to-peak filtering of nonlinear stochastic structures. The reader is brought to 6 sensible 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 useful for a formal appreciation of the textual content: a simple advent to stochastic keep watch over approaches, elements of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback keep watch over difficulties of stochastic switched platforms with dwell-time. complicated subject matters up to the mark and Estimation of State-Multiplicative Noisy structures might be of curiosity to engineers engaged on top of things platforms study and improvement, to graduate scholars focusing on stochastic keep watch over idea, and to utilized mathematicians attracted to keep an eye on difficulties. The reader is anticipated to have a few acquaintance with stochastic keep watch over thought and state-space-based optimum keep watch over thought and strategies for linear and nonlinear systems.

Table of Contents

Cover

Advanced issues 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 procedure for behind schedule Systems

1.2.1 Continuous-Time Case

1.2.2 Discrete-Time Case

1.3 Non Linear regulate 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 strategies - 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 platforms - H-infinity regulate 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 powerful 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 powerful 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 strong 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 behind schedule Systems

2.7.1 Stochastic Output-Feedback regulate - The Nominal Case

2.7.2 instance - Output-Feedback Control

2.7.3 strong Stochastic Output-Feedback keep watch over - 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 behind schedule Stochastic Reduced-Order H keep watch over 8

3.4 Conclusions

4 monitoring keep an eye on 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 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 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 keep an eye on 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 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 powerful L-infinity-Induced keep watch over and Filtering

12.1 Introduction

12.2 challenge formula and Preliminaries

12.3 balance and P2P Norm sure 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 regulate of Switched Systems

13.4 Non Linear structures: size Output-Feedback Control

13.5 Discrete-Time Non Linear structures: l2-Gain

13.6 L-infinity keep an eye on and Estimation

A Appendix: Stochastic keep an eye on methods - uncomplicated Concepts

B The LMI Optimization Method

C Stochastic Switching with reside Time - Matlab Scripts

References

Index

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**Extra resources for Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems**

**Example text**

10). 49). 49) ⎡ and where ¯ Y ] 0 0 0 h f E T [X ¯ Y] 0 0 0 0 Υ2T = E0T [X 0 ¯ Y ] 0 0 0 h f E T [X ¯ 0] 0 0 0 0 Υ3T = E0T [X 0 ¯ Y ] 0 0 0 h f E T [X ¯ Y] 0 0 0 0 Υ4T = E1T [X 1 T T T , , . 45). 12). 12. 12). 50). 51) ˜ f hΥi,14 . 47). 5 1 , d = 0. e α ¯ = 0). 11 . 1 Stochastic Output-Feedback Control – The Nominal Case In this section we address the dynamic output-feedback control problem of the delayed state-multiplicative uncertain noisy system [59]. 7). 52) Gξ(t)dβ(t) + F˜ ξ(t)dζ(t), ξ(θ) = 0, over[−h 0], ˜ z˜(t) = Cξ(t), with the following matrices: Aˆ0 = ˜ = H H0 0 0 A0 B2 Cc Bc C2 Ac ˜= , G G0 0 0 , Aˆ1 = , F˜ = A1 0 Bc C¯2 0 0 0 Bc F 0 ˜= , B B1 0 0 Bc D21 , C˜ = [C1 D12 Cc ].

1a,c) with B2 = 0 and D12 = 0. 4. 3. The delay independent BRL is readily obtained from the latter LMI by deleting the 3rd and 5th column and row blocks in Γ and by choosing Qm = 0 in Ψ˜11 and Ψ¯12 . 12). 6. 12). 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.

E α ¯ = 0). 11 . 1 Stochastic Output-Feedback Control – The Nominal Case In this section we address the dynamic output-feedback control problem of the delayed state-multiplicative uncertain noisy system [59]. 7). 52) Gξ(t)dβ(t) + F˜ ξ(t)dζ(t), ξ(θ) = 0, over[−h 0], ˜ z˜(t) = Cξ(t), with the following matrices: Aˆ0 = ˜ = H H0 0 0 A0 B2 Cc Bc C2 Ac ˜= , G G0 0 0 , Aˆ1 = , F˜ = A1 0 Bc C¯2 0 0 0 Bc F 0 ˜= , B B1 0 0 Bc D21 , C˜ = [C1 D12 Cc ]. 54) where ˜ Aˆ0 + m) + (Aˆ0 + m)T Q ˜+ Υ11 = Q( 1 R1 .