Semigroup theory with applications to systems and control
著者
書誌事項
Semigroup theory with applications to systems and control
（Pitman research notes in mathematics series, 246）
Longman Scientific & Technical , Wiley, c1991
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- : us
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注記
Bibliographical references: p. 275-282
内容説明・目次
内容説明
Semigroup theory provides a unified and a powerful tool for the study of differential equations on Banach space covering systems described by ordinary differential equations, partial differential equations, functional differential equations and combinations thereof. In recent years, among many other applications, semigroup theory has been widely used in the study of control and stability of systems governed by differential equations on Banach space. This monograph is an introduction to semigroup theory with applications to control and stability. Chapters I-VI cover semigroup theory with applications to linear, nonlinear and stochastic differential equations on Banach spaces. Chapter VII is devoted to a brief study of stability, control and filtering of infinite dimensional systems. The monograph is an outgrowth of a series of lectures given by the author at the department of mathematics of the University of Western Australia in Perth in the summer of 1988.
目次
- Part 1 Basic properties of semigroups: uniformly continuous semigroups
- strongly continuous semigroups
- some elemtary examples. Part 2 Generation theorems for semigroups: contraction or dissipative semigroups
- general CO-semigroups
- adjoint semigroups
- integrated semigroups
- examples. Part 3 Semigroups with special properties: CO-groups
- differentiable and analytic semigroups
- fractional powers of closed operators
- compact semigroups. Part 4 Perturbation theory of semigroups: bounded perturbation of general CO-semigroups
- relatively bounded perturbation of analytic semigroups
- relatively bounded perturbation of dissipative semigroups
- Trotter-Kato approximation theory of semigroups. Part 5 Differential equations on Banach space: linear evolution equations
- semilinear and quasilinear evolution equations
- integrated semigroups and evolution equations. Part 6 Stochastic differential equations on Banach space: stochastic integrals
- linear stochastic evolution equations
- nonlinear stochastic evolution equations. Part 7 Applications to systems and control: stability controllability and stabilizability
- stability of measures
- system identification
- optimal control
- linear filtering and partially observed controls
- optimal control of nonlinear stochastic systems.
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