Mathematical Methods in Robust Control of Linear Stochastic Systems, 2nd Edition

  • Published By:
  • ISBN-10: 1461486637
  • ISBN-13: 9781461486633
  • DDC: 629.8312
  • Grade Level Range: College Freshman - College Senior
  • 442 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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This second edition includes recent results in the control of linear stochastic systems, including: A unified and abstract framework for Riccati type equations arising in the stochastic control; Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states; Mixed H2 / H∞ control problem and numerical procedures; Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states; Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps;and H∞ reduced order filters for stochastic systems. The book is written for graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis. Review of first edition: "This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems.…Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources." (Mathematical Reviews, Issue 2007 m). "The book is very well written and organized.…is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances." (SIAM Review, Vol. 49 (3), 2007)

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Preface to the First Edition.
1: Preliminaries to Probability Theory and Stochastic Differential Equations.
2: Linear Differential Equations with Positive Evolution on Ordered Banach Spaces.
3: Exponential Stability in Mean Square.
4: Structural Properties of Linear Stochastic Systems.
5: A Class of Nonlinear Differential Equations on an Ordered Linear Space of Symmetric Matrices with Applications to Riccati Differential Equations of Stochastic Control.
6: Linear Quadratic Optimization Problems for Linear Stochastic Systems.
7: Stochastic H2 Optimal Control.
8: Stochastic Version of Bounded Real Lemma and Applications.
9: Robust Stabilization of Linear Stochastic Systems.