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The book addresses the control issues such as stability analysis,
control synthesis and filter design of Markov jump systems with the
above three types of TPs, and thus is mainly divided into three
parts. Part I studies the Markov jump systems with partially
unknown TPs. Different methodologies with different conservatism
for the basic stability and stabilization problems are developed
and compared. Then the problems of state estimation, the control of
systems with time-varying delays, the case involved with both
partially unknown TPs and uncertain TPs in a composite way are also
tackled. Part II deals with the Markov jump systems with piecewise
homogeneous TPs. Methodologies that can effectively handle control
problems in the scenario are developed, including the one coping
with the asynchronous switching phenomenon between the currently
activated system mode and the controller/filter to be designed.
Part III focuses on the Markov jump systems with memory TPs. The
concept of -mean square stability is proposed such that the
stability problem can be solved via a finite number of conditions.
The systems involved with nonlinear dynamics (described via the
Takagi-Sugeno fuzzy model) are also investigated. Numerical and
practical examples are given to verify the effectiveness of the
obtained theoretical results. Finally, some perspectives and future
works are presented to conclude the book.
This book focuses on the basic control and filtering synthesis
problems for discrete-time switched linear systems under
time-dependent switching signals. Chapter 1, as an introduction of
the book, gives the backgrounds and motivations of switched
systems, the definitions of the typical time-dependent switching
signals, the differences and links to other types of systems with
hybrid characteristics and a literature review mainly on the
control and filtering for the underlying systems. By summarizing
the multiple Lyapunov-like functions (MLFs) approach in which
different requirements on comparisons of Lyapunov function values
at switching instants, a series of methodologies are developed for
the issues on stability and stabilization, and l2-gain performance
or tube-based robustness for l disturbance, respectively, in
Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and
filtering problems for the time-dependent switched linear systems
with either polytopic uncertainties or measurable time-varying
parameters in different sense of disturbances. The asynchronous
switching problem, where there is time lag between the switching of
the currently activated system mode and the controller/filter to be
designed, is investigated in Chapter 6. The systems with various
time delays under typical time-dependent switching signals are
addressed in Chapter 7.
The book addresses the control issues such as stability analysis,
control synthesis and filter design of Markov jump systems with the
above three types of TPs, and thus is mainly divided into three
parts. Part I studies the Markov jump systems with partially
unknown TPs. Different methodologies with different conservatism
for the basic stability and stabilization problems are developed
and compared. Then the problems of state estimation, the control of
systems with time-varying delays, the case involved with both
partially unknown TPs and uncertain TPs in a composite way are also
tackled. Part II deals with the Markov jump systems with piecewise
homogeneous TPs. Methodologies that can effectively handle control
problems in the scenario are developed, including the one coping
with the asynchronous switching phenomenon between the currently
activated system mode and the controller/filter to be designed.
Part III focuses on the Markov jump systems with memory TPs. The
concept of -mean square stability is proposed such that the
stability problem can be solved via a finite number of conditions.
The systems involved with nonlinear dynamics (described via the
Takagi-Sugeno fuzzy model) are also investigated. Numerical and
practical examples are given to verify the effectiveness of the
obtained theoretical results. Finally, some perspectives and future
works are presented to conclude the book.
This book focuses on the basic control and filtering synthesis
problems for discrete-time switched linear systems under
time-dependent switching signals. Chapter 1, as an introduction of
the book, gives the backgrounds and motivations of switched
systems, the definitions of the typical time-dependent switching
signals, the differences and links to other types of systems with
hybrid characteristics and a literature review mainly on the
control and filtering for the underlying systems. By summarizing
the multiple Lyapunov-like functions (MLFs) approach in which
different requirements on comparisons of Lyapunov function values
at switching instants, a series of methodologies are developed for
the issues on stability and stabilization, and l2-gain performance
or tube-based robustness for l disturbance, respectively, in
Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and
filtering problems for the time-dependent switched linear systems
with either polytopic uncertainties or measurable time-varying
parameters in different sense of disturbances. The asynchronous
switching problem, where there is time lag between the switching of
the currently activated system mode and the controller/filter to be
designed, is investigated in Chapter 6. The systems with various
time delays under typical time-dependent switching signals are
addressed in Chapter 7.
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