-Preliminaries on Probability Theory and Stochastic Differential Equations. - Linear Differential Equations with Positive Evolution on Ordered Banach Spaces.- Exponential Stability in Mean Square. - Structural Properties of Linear Stochastic Systems. -A Class of Nonlinear Differential Equations on an Ordered Space of Symmetric Matrices with Application to Ricati Differential Equations of Stochastic Control. - Linear Quadratic Optimization Problems.- H2 Optimal Control of Linear Stochastic Systems. -Stochastic Version of Bounded Real Lemma and Applications. - Robust stabilization of linear stochastic systems.
This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are:
- 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 / H8 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
- H8 reduced order filters for stochastic systems
The book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis.
From Reviews of the 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.
(George Yin, Mathematical Reviews, Issue 2007 m)
Updates the previous edition to include recent results in robust control of linear stochastic systems
Presents the treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations
Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations