Yonggui Kao

A sliding mode approach to H ∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems

This paper is focused on designing an H ∞ sliding-mode control for a class of neutral-type stochastic systems with Markovian switching parameters and nonlinear uncertainties. An H ∞ non-fragile observer subjected to the transition rates of the switching mode is firstly constructed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. Then, the state-estimation-based sliding mode control law is designed to guarantee the reachability of the sliding surface in finite time interval. Furthermore, a stochastic stability criterion is established for all admissible uncertainties, which can guarantee the error system and sliding mode dynamics to be asymptotically stochastic stable with a given disturbance attenuation level. Finally, an example is provided to illustrate the efficiency of the proposed method.

Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is known. In terms of a set of coupled linear matrix inequalities (LMIs), a sufficient condition is established to ensure the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent state-feedback controller is derived to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.

Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability

The problem of global exponential stability in mean square of delayed Markovian jump fuzzy cellular neural networks (DMJFCNNs) with generally uncertain transition rates (GUTRs) is investigated in this paper. In this GUTR neural network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than the existing ones. By constructing suitable Lyapunov functionals, several sufficient conditions on the exponential stability in mean square of its equilibrium solution are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and efficiency of our results.

Input-to-state stability for discrete-time nonlinear switched singular systems

Discrete-time nonlinear switched singular systems (SSSs) are investigated.The input-to-state stability (ISS) problems for discrete-time nonlinear SSSs are concerned.The ISS criteria are obtained via average dwell time approach and iterative algorithm of discrete-time systems.The switching rules are optimized and designed. This paper investigates the input-to-state stability (ISS) problems for a class of discrete-time nonlinear switched singular systems (SSSs). Two novel ISS criteria are proposed based on average dwell time (ADT) approach and iterative algorithm of discrete-time systems (IADS). In particular, the following two cases are considered for the underlying systems: the first case is that all the sub-systems are exponentially stable, and the other case is that only a few sub-systems are exponentially stable. The corresponding ISS criteria are obtained to guarantee that the closed-loop systems are input-to-state stable via ADT approach and IADS. We neither construct a specific Lyapunov function for ISS in the proof process of the stability criteria nor design a specific structure of the control inputs. The design deficit of the switching controllers is optimized and the design difficulty of the switching controllers is reduced via the proposed criteria. Finally, two numerical examples are provided to illustrate the feasibility of the results obtained.

Soft variable structure controller design for singular systems

Abstract A novel soft variable structure control (SVSC) scheme is addressed for a class of singular systems under I-controllable in this paper. The structural features of SVSC with differential equations are investigated. The stability of singular systems based on SVSC scheme is guaranteed by an equivalent characterization theory, and then a soft variable structure controller is designed. The concrete algorithm of SVSC with differential equations is proposed. The developed SVSC law for singular systems is carried out for the purpose of achieving rapid regulative rate, and shortening arrival time. Moreover, system chattering can be attenuated in the process of approaching to the equilibrium state. Finally, a simulation example is provided to verify the feasibility of the proposed scheme.

H ∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters

This paper is devoted to the investigation of H ∞ sliding mode control (SMC) for uncertain neutral stochastic systems with Markovian jumping parameters and time-varying delays. A sliding surface functional is firstly constructed. Then, the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite-time interval. The sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency of the proposed method.

Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching

In this paper, based on the Lyapunov second method and Razumikin techniques, we establish some novel criteria on pth moment exponential stability, almost exponential stability and instability of impulsive stochastic functional differential equations (ISFDEs) with Markovian switching. The findings show that impulsive stochastic functional equations with Markovian switching can be exponentially stabilized by impulses. Finally, an example is presented to illustrate the effectiveness and efficiency of the obtained results.

Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates

This paper is devoted to investigating the stability and stabilisation problems for continuous-time mode-dependent singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). First, we establish a sufficient condition in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the systems to be regular, impulse-free and stochastically stable. Then, we design a mode-dependent state-feedback controller to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.

Controller design for time-delay system with stochastic disturbance and actuator saturation via a new criterion

Abstract This paper deals with the problem of controller design for time-delay system with stochastic disturbance and actuator saturation. By use of more appropriate Lyapunov–Krasovskii functional (LKF) and a new criterion for the domain of attraction, less conservative conditions for stochastic stability are proposed. Then, the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome. These sufficient conditions are derived in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the given results.

Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances

In this paper, a sliding mode control (SMC) of uncertain discrete singular systems with external disturbances and time-varying delays is under consideration. By use of the free weighting matrices and the Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is given in strict linear matrix inequality (LMI) format to guarantee the sliding mode dynamics to be admissible (regular, causal and stable). Furthermore, a proposed SMC law and an adaptive SMC law are synthesized to make sure that the trajectories of system can be driven to a region near equilibrium point in finite time. Finally, a numerical example is designed to display the effectiveness of the control scheme. All these results are expected to propose a new approach for the research on SMC of discrete time-delay singular systems.