Stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities

This paper considers the stochastic stability and stabilization of discrete-time singular Markovian jump systems with partially unknown transition probabilities. Firstly, a set of necessary and sufficient conditions for the stochastic stability is proposed in terms of LMIs, then a set of sufficient conditions is proposed for the design of a state feedback controller to guarantee that the corresponding closed-loop systems are regular, causal, and stochastically stable by employing the LMI technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approaches

Robust Quantized Generalized H

This paper deals with the problem of robust generalized H2 filter design for uncertain discrete-time fuzzy systems with output quantization. Firstly, the outputs of the system are quantized by a memoryless logarithmic quantizer before being transmitted to a filter. Then, attention is focused on the design of a generalized H2 filter to mitigate quantization effects, such that the filtering error systems ensure the robust stability with a prescribed generalized H2 noise attenuation level. Via applying Finsler lemma to introduce some slack variables and using the fuzzy Lyapunov function, sufficient conditions for the existence of a robust generalized H2 filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the T-S fuzzy descriptor systems are developed. A two step design is ?rst developed to obtain the observer gains and coef?cients in the switching function using linear matrix inequalities, and the results are used to facilitate the development of a single step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method

Robust stability of uncertain discrete-time singular fuzzy systems

This paper considers the problem of robust stability analysis of uncertain discrete-time singular fuzzy systems described by a class of extended Takagi-Sugeno fuzzy dynamic models with time-varying norm-bounded parameter uncertainties. A sufficient condition ensuring a discrete singular fuzzy system to be regular, causal and stable is proposed in terms of a set of linear matrix inequalities. Based on this, a robust stability condition is obtained. Both of these conditions can be checked by using recently developed algorithms in solving LMIs. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions. © 2007 Elsevier B.V. All rights reserved.link_to_subscribed_fulltex