Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided

H∞ model reduction for discrete-time Markovian jump systems with deficient mode information

This paper investigates the problem of H∞ model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new H∞ performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for the H∞ model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods

Robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process

This paper investigates the problem of robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robust L2 -L8 filter is designed which guarantees that the resulting error dynamic system is robustly stochasticallystable and satisfies a prescribed L2 - L∞ performance index. A numerical example is given to illustrate the effectiveness of the developed techniques

Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results

Stability Analysis for Stochastic Markovian Jump Reaction-Diffusion Neural Networks with Partially Known Transition Probabilities and Mixed Time Delays

The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results

Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates

This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. Based on linear matrix inequalities, the quantized state-feedback controller is formulated to ensure the closed-loop system is stable in mean square. Finally, a numerical example is presented to verify the validity of the developed theoretical results