Download Analysis and Design of Singular Markovian Jump Systems by Guoliang Wang, Qingling Zhang, Xinggang Yan PDF

By Guoliang Wang, Qingling Zhang, Xinggang Yan

This monograph is an updated presentation of the research and layout of singular Markovian leap structures (SMJSs) within which the transition expense matrix of the underlying structures is mostly doubtful, in part unknown and designed. the issues addressed comprise balance, stabilization, H∞ regulate and filtering, observer layout, and adaptive regulate. functions of Markov strategy are investigated by utilizing Lyapunov thought, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, between different techniques.

Features of the e-book include:

· learn of the soundness challenge for SMJSs with basic transition fee matrices (TRMs);

· stabilization for SMJSs by way of TRM layout, noise keep watch over, proportional-derivative and in part mode-dependent keep watch over, when it comes to LMIs with and with out equation constraints;

· mode-dependent and mode-independent H∞ keep watch over strategies with improvement of one of those disordered controller;

· observer-based controllers of SMJSs within which either the designed observer and controller are both mode-dependent or mode-independent;

· attention of strong H∞ filtering by way of doubtful TRM or clear out parameters resulting in a mode for absolutely mode-independent filtering

· improvement of LMI-based stipulations for a category of adaptive country suggestions controllers with almost-certainly-bounded envisioned errors and almost-certainly-asymptotically-stable corresponding closed-loop process states

· purposes of Markov approach on singular structures with norm bounded uncertainties and time-varying delays

Analysis and layout of Singular Markovian leap Systems includes worthwhile reference fabric for tutorial researchers wishing to discover the world. The contents also are compatible for a one-semester graduate course.

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Additional info for Analysis and Design of Singular Markovian Jump Systems

Example text

IEEE Trans Autom Control 37:38–53 3. Huang LR, Mao XR (2010) On almost srue stability of hybrid stochastic systems with modedependent interval delays. IEEE Trans Autom Control 55:1946–1952 4. Mao XR (1999) Stability of stochastic differential equations with Markovian switching. Stochastic Processes their Appl 79:45–67 5. Mao XR (2002) Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans Autom Control 47:1604–1612 6. Boukas EK, Shi P, Benjelloun K (1999) On robust stabilization of uncertain linear systems with jump parameters.

Then, the robust stability of Markovian jump singularly perturbed systems with uncertain switchings and nonlinear perturbations for any perturbation parameter ω ∞ (0, ω¯ ] are solved by an LMI approach. Instead of containing ω, such conditions guaranteeing the existence and uniqueness of a solution as well as stochastic admissibility, are established by choosing an ω-dependent Lyapunov function and only depend on stability bound ω¯ . It is worth mentioning that the stability results proposed in this chapter will play important roles in dealing with other problems.

In some cases, an appropriate TRM may be selected for MJSs. 5) are linear to matrix Pi . 5) turns out to be bilinear due to the product terms of non-singular matrix Pi and elements in Π . When similar problem is discussed in [15], the positive-definite property of Pi for normal state-space MJSs plays important roles in system analysis and synthesis. Due to the singular derivative matrix and the only non-singular Lyapunov matrix, the property of Pi is not true for SMJSs. Thus, such problems should be reconsidered for SMJSs.

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