By Eli Gershon

Complicated themes up to the mark and Estimation of State-Multiplicative Noisy platforms starts off with an creation 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 provided and solved for nominal and unsure stochastic platforms, through the input-output procedure. It offers recommendations to the issues of state-feedback, filtering, and measurement-feedback regulate 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 watch over also are offered and solved. the second one a part of the monograph matters non-linear stochastic kingdom- multiplicative structures 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 situations. The e-book additionally describes designated themes comparable to stochastic switched platforms with reside time and peak-to-peak filtering of nonlinear stochastic platforms. 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 ebook is rounded out through a three-part appendix containing stochastic instruments important for a formal appreciation of the textual content: a easy advent to stochastic keep an eye on techniques, points 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. complex themes on top of things and Estimation of State-Multiplicative Noisy structures may be of curiosity to engineers engaged up to the mark structures study and improvement, to graduate scholars focusing on stochastic keep watch over idea, and to utilized mathematicians drawn to regulate difficulties. The reader is anticipated to have a few acquaintance with stochastic keep an eye on idea and state-space-based optimum keep watch over concept and strategies for linear and nonlinear systems.

Table of Contents

Cover

Advanced subject matters on top of things 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 method for behind schedule Systems

1.2.1 Continuous-Time Case

1.2.2 Discrete-Time Case

1.3 Non Linear keep watch over 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 methods - 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 strong 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 not on time State-Multiplicative structures - 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 strong State-Feedback keep watch over - 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 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 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 strong 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 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 keep watch over 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 platforms - size 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 watch over 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 regulate of Stochastic Switched structures with reside 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 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 keep watch over 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 regulate and Estimation

A Appendix: Stochastic regulate strategies - simple Concepts

B The LMI Optimization Method

C Stochastic Switching with reside Time - Matlab Scripts

References

Index

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**Sample text**

10). 2. 25) ⎢ ⎥<0 ⎢ ∗ ∗ ⎥ ∗ − Q h QE h QE f f 0 f 1 ⎢ ⎥ ⎣ ∗ ∗ ⎦ ∗ ∗ − 1 In 0 ∗ ∗ ∗ ∗ ∗ − 2 In where Ψˆ11 Ψˆ12 Ψˆ14 Ψˆ22 Ψˆ24 = QA0 + Qm + AT0 Q + QTm + = QA1 − Qm + αG ¯ T QH, = h f AT0 Q + h f QTm , ¯ 1T H ¯1 = −R1 + H T QH + 2 H T T = h f A1 Q − h f Qm . 2. The above result provides a delay dependent stability condition. A corresponding delay independent (but rate dependent) result is readily obtained by choosing m = 0 and f → 0. 16). 16) is guaranteed if there exist matrices Q > 0, R1 > 0 and scalars 1 , 2 that satisfy the following LMI.

In other words: N ¯= Ω N ¯ i fi Ω i=1 , fi = 1 i=1 , fi ≥ 0. 3). Our objective is to ﬁnd a state-feedback polytope Ω control law u(t) = Kx(t) that achieves JE < 0, for the worst-case of the pro˜ 2 ([0, ∞); Rq ) and for a prescribed scalar γ > 0. 6). 6) is negative for all nonzero w(t), n(t) where ˜ 2 ([0, ∞); Rq ), n(t) ∈ L ˜ 2 ([0, T ]; Rp ). 3). 7) that achieves JE < 0, for the worst-case distur˜ 2 ([0, ∞); Rq ) and measurement noise n(t) ∈ L ˜ 2 ([0, T ]; Rp ), bance w(t) ∈ L Ft Ft and for a prescribed scalar γ > 0.

4 1 T R1 + Gi QGi . 1a,c) with B2 = 0 and D12 = 0 and the following index of performance ∞ Δ JB = E{ 0 ∞ ||z(t)||2 dt − γ 2 ||w(t)||2 dt}. 24) is satisﬁed, we seek a condition that guarantees the following: ∞ E [LV + z T (t)z(t) − γ 2 wT (t)w(t)]dt < 0, 0 where in the expression for E{LV } the operators Δ1 and Δ2 are used. 4. 1a,c) with B2 = 0 and D12 = 0. 1 = QA0 + Qm + AT0 Q + QTm + = QA1 − Qm + α ¯ GT QH, = h f AT0 Q + h f QTm , = −R1 + H T QH, = h f AT1 Q − h f QTm . 10). 5. 1a,c) with B2 = 0 and D12 = 0.