Preface
As a kind of special stochastic system, multi-model jumping system has received
in-depth research, and a lot of innovative results have been achieved due to the
profound influence and significance in theoretical and practical aspects.
Multi-model jumping system that follows Markov switching laws was firstly proposed by Krasovskii and Lidskii in the 1960s. The modes of multi-model jumping
systems are described by continuous-time and discrete-state Markov process, and
the states of the system are described by the state space equations under each mode.
In the past few decades, there have been a lot of research results on multi-model
jumping systems, which mainly focus on stochastic stability, stochastic stabilization, controller design and comprehensive analysis, robust filtering and fault
detection. Comparing with the linear multi-model jumping systems, the research of
nonlinear multi-model jumping systems is not well-considered, which is mainly due
to the complexity of the nonlinearities. Fortunately, the control problem of nonlinear multi-model jumping systems becomes relatively easy with the development
of Takagi-Sugeno (T-S) fuzzy technology and linear differential inclusion (LDI)based neural network technology. Although a lot of theoretical research results have
been obtained for multi-model jumping systems, the study on this kind of stochastic
systems is still under development. The research of multi-model jumping systems
needs further improvement and discussion due to the fact that intact research systems have not formed in theoretical aspects and technical aspects.
On the other hand, as important branches of system control theory and signal
processing, many researchers have carried out systematic research on state estimation and filtering. For the dynamical systems with uncertain parameters in many
industrial applications, the robust filtering scheme is the best solution to such a
situation. The main robust filtering methods include H ∞ estimation, L 2 -L ∞ estimation, L 1 estimation, robust dissipative estimation, robust guaranteed performance
filtering, robust passive filtering, etc. Furthermore, the requirements for equipment
safety and reliability are becoming more and more important with the increasing
complexity of modern engineering systems. Fault detection and diagnosis is one
v
As a kind of special stochastic system, multi-model jumping system has received
in-depth research, and a lot of innovative results have been achieved due to the
profound influence and significance in theoretical and practical aspects.
Multi-model jumping system that follows Markov switching laws was firstly proposed by Krasovskii and Lidskii in the 1960s. The modes of multi-model jumping
systems are described by continuous-time and discrete-state Markov process, and
the states of the system are described by the state space equations under each mode.
In the past few decades, there have been a lot of research results on multi-model
jumping systems, which mainly focus on stochastic stability, stochastic stabilization, controller design and comprehensive analysis, robust filtering and fault
detection. Comparing with the linear multi-model jumping systems, the research of
nonlinear multi-model jumping systems is not well-considered, which is mainly due
to the complexity of the nonlinearities. Fortunately, the control problem of nonlinear multi-model jumping systems becomes relatively easy with the development
of Takagi-Sugeno (T-S) fuzzy technology and linear differential inclusion (LDI)based neural network technology. Although a lot of theoretical research results have
been obtained for multi-model jumping systems, the study on this kind of stochastic
systems is still under development. The research of multi-model jumping systems
needs further improvement and discussion due to the fact that intact research systems have not formed in theoretical aspects and technical aspects.
On the other hand, as important branches of system control theory and signal
processing, many researchers have carried out systematic research on state estimation and filtering. For the dynamical systems with uncertain parameters in many
industrial applications, the robust filtering scheme is the best solution to such a
situation. The main robust filtering methods include H ∞ estimation, L 2 -L ∞ estimation, L 1 estimation, robust dissipative estimation, robust guaranteed performance
filtering, robust passive filtering, etc. Furthermore, the requirements for equipment
safety and reliability are becoming more and more important with the increasing
complexity of modern engineering systems. Fault detection and diagnosis is one
v