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In this paper, (reverse) mode-dependent average dwell time (MDADT) method combined with multiple incremental Lyapunov functions is utilized to investigate the stochastic incremental input-to-state stability (SIISS) of stochastic switched systems. The sufficient conditions in terms of the (reverse) MDADT scheme are extracted to ensure SIISS, while it is shown that the SIISS can still be achieved even if all subsystems are not stochastically incrementally input-to-state stable. In particular, an incremental supply rate is introduced to obtain sufficient conditions to ensure SIISS for stochastic feedback interconnected switched systems. Specifically, when the stochastic switched systems are composed of some SIISS and non-SIISS subsystems, the (reverse) MDADT method is employed to establish a relationship between these two kinds of subsystems to ensure SIISS for the stochastic switched systems. Two examples are presented to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper studies the dissipative control problem for two-dimensional (2-D) switched discrete-time linear system represented by Fornasini–Marchesini local state-space (FMLSS) model via dwell-time-dependent Lyapunov function (DTDLF) approach. Consider the definition of (Q, S, R)- α -dissipativity for 2-D switched discrete FMLSS model in triangular region and based on the DTDLF approach, we first give the linear matrix inequality (LMI)-based sufficient condition on asymptotic stability for the 2-D switched discrete FMLSS model and then propose the LMI-based sufficient condition which can guarantee the given 2-D switched system to be asymptotically stable and strictly (Q, S, R)- α -dissipative. Furthermore, the dwell-time-dependent dissipative state-feedback controller is designed, and the LMI-based sufficient condition for designing such controller is proposed. Besides, dwell-time-dependent passive state-feedback controller and dwell-time-dependent H ∞ state-feedback controller could be derived as the special cases of dissipative control from the established result. Finally, illustrative examples are depicted to verify the efficiency and superiority of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-region dissipative control of two-dimensional (2-D) linear discrete-time Roesser model. Firstly, we define a concept of finite-region -μ-dissipativity. Then, by using Lyapunov function and establishing special recursive formulas, a new sufficient condition with a simpler form is formulated which ensures the resulting closed-loop system is finite-region bounded. Based on this, we propose the sufficient condition for finite-region -μ-dissipativity of closed-loop system. Furthermore, the sufficient condition that can be verified by linear matrix inequalities (LMIs) for designing the finite-region -μ-dissipative state-feedback controller is given. Moreover, the finite-region passive control, finite-region control and mixed finite-region passive and control can be obtained as the special cases from the established result. Finally, numerical examples are presented to display the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the incremental H ∞ control for switched nonlinear systems by using a state-dependent switching law and an average dwell time approach incorporated with multiple Lyapunov functions. Even if all subsystems are unstable, a sufficient condition for the incremental H ∞ control problem to be solvable is derived based on the design state-dependent switching law. Furthermore, when all subsystems are incrementally globally asymptotically stable (IGAS), the switched nonlinear system under the average dwell time scheme is IGAS and possesses a weighted incremental L 2 -gain. Then, we extend this result to the case where both IGAS subsystems and unstable subsystems coexist, if the activation time ratio between IGAS subsystems and unstable ones is not less than a specified constant, sufficient conditions for the weighted incremental H ∞ performance of the switched system are guaranteed. Two numerical examples are given to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Exponentially incremental (Q,S,R)-dissipativityand incremental stability for switched time-varying nonlinear systems are studied whose subsystems are not required to be exponentially incrementally (Q,S,R)-dissipative. The sufficient conditions for switched time-varying nonlinear systems to be exponentially incrementally (Q,S,R)-dissipative are presented by the design of state-dependent switching laws. Incremental stability for switched time-varying nonlinear systems are derived based on exponentially incremental (Q,S,R)-dissipativity. Exponentially incremental (Q,S,R)-dissipativity is shown to be preserved under feedback interconnection by the design of a composite state-dependent switching law. Two simulation examples are provided to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the H ∞ filtering problem for two-dimensional T-S fuzzy systems. Sufficient conditions for the solvability of this problem are obtained by using basis-dependent Lyapunov functions. By considering the measured output as an independent variable with respect to the state variable and the disturbance input, a new method for designing two-dimensional H ∞ filters is presented. Moreover, it has been shown that the proposed method is equivalent to the conventional one. Therefore, the proposed method does not lead to any conservativeness that may be caused by separately considering the measured output, the state variable, and the disturbance input. In converting the parameterized linear matrix inequalities (PLMI) into LMI constraints, attention is focused on the reduction of the number of LMI-based conditions. On the basis of the proposed theorem, the number of LMI-based conditions is reduced to r3 from r3( r + 1)2 ∕ 4 by the conventional method. Thus, the computational advantage is obvious for fuzzy systems with large number of fuzzy rules. Simulation results have demonstrated the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]