System Theory

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

By Guoliang Wang, Qingling Zhang, Xinggang Yan

This monograph is an up to date presentation of the research and layout of singular Markovian leap structures (SMJSs) during which the transition price matrix of the underlying platforms is usually doubtful, in part unknown and designed. the issues addressed contain balance, stabilization, H∞ regulate and filtering, observer layout, and adaptive regulate. purposes of Markov technique are investigated through the use of Lyapunov thought, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, between different techniques.

Features of the ebook include:

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

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

· mode-dependent and mode-independent H∞ keep watch over options with improvement of a kind of disordered controller;

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

· attention of sturdy H∞ filtering when it comes to doubtful TRM or clear out parameters resulting in a mode for completely mode-independent filtering

· improvement of LMI-based stipulations for a category of adaptive kingdom suggestions controllers with almost-certainly-bounded expected blunders and almost-certainly-asymptotically-stable corresponding closed-loop approach states

· purposes of Markov technique on singular platforms with norm bounded uncertainties and time-varying delays

Analysis and layout of Singular Markovian bounce Systems comprises worthy reference fabric for tutorial researchers wishing to discover the world. The contents also are appropriate for a one-semester graduate course.

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Additional resources for Analysis and Design of Singular Markovian Jump Systems

Example text

75) with γi = 1, i = 1, 2. 4 By methods in [21–23, 30], there is no information on stability bound ω¯ . 5229. 5π˜ 21 respectively. 3219 which guarantees that the aforementioned system is exponentially mean-square stable for any ω ∞ (0, ω¯ ]. 3 Consider the following singularly perturbed system controlled by a DC motor, which is illustrated in Fig. 1. 3 Robust Stability 49 Fig. 1 DC motor controlling an inverted pendulum where {rt , t ∈ 0} is a Markov process taking values in a finite set S = {1, 2}.

Matrix E ∞ Rn×n may be singular, which is assumed to be rank(E) = r ≥ n. A1 (rt ), A2 (rt ), A3 (rt ), A4 (rt ), B1 (rt ) and B2 (rt ) are known matrices of compatible dimensions. 11). 74) where γi > 0, Fki and G ki are constant matrices with appropriate dimensions. 77) ⎦ F1 (rt ) G 1 (rt ) . 73) will lead to ill-conditioned problem in system analysis and synthesis when ω tends to be zero. 73) belongs to singularly perturbed descriptor systems whose robust stability was considered in [26]. 73).

54). This completes the proof. 11 gives an approach of designing a stabilizing TRM, in which the corresponding matrix Pi is not necessary positive-definite. In addition, this approach can be extended to the other system analysis and synthesis problems easily. 11 is used to deal with normal statespace MJSs with TRM designed. In this sense, this theorem can be considered as an extension of normal state-space MJSs to SMJSs. 56) Wi Z i = I. 51). 60) Wi Z i = I. 51). 63) Wi Z i = I. 51) is used to compute a stabilizing SPRM.

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