Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates

This paper considers the problem of stabilization for a class of stochastic Markov jump distributed delay systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov function, a state memory feedback controller is designed to guarantee that the resulted closed-loop constrained systems are mean-square stochastic asymptotically stable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Filtering-based robust fault detection of fuzzy jump systems

This paper studies the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markov jump systems with state delays and parameter uncertainties. By means of Takagi-Sugeno fuzzy models, the dynamics of filtering error generator and the fuzzy RFDF system are constructed. With the aid of the selected weighting matrix function, the design objective is to find an optimal RFDF which results in a minimal difference between the reference model (ideal solution) and the RFDF (real solution) to be designed. A sufficient condition is firstly established on the stochastic stability by using stochastic Lyapunov-Krasovskii functional approach. Then in terms of linear matrix inequalities techniques, sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as an optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences.     

Observer-based fault detection for networked control systems with network Quality of Services

This paper addresses the problem of the fault detection for linear time-invariant systems over data networks with limited network Quality of Services (QoS). An integrated index _ηk${\eta }_k$, which related with data dropout, network-induced delay and error sequence, is presented to described the non-ideal QoS, the probabilistic switching between different _ηk${\eta }_k$ is assumed to obey a homogeneous Markovian chain. Then by view of the augmented matrices approach, the fault detection error dynamic systems are transferred to Markov jumping systems (MJSs). With the developed model and using the bounded real lemma (BRL) for MJSs, an _H∞$H_{\infty }$ observer-based fault detection filter is established in terms of linear matrix inequalities (LMIs) to guarantee that the error between the residual and the weighted faults is made as small as possible. A simulation example is provided to show the effectiveness of the present methods.     

Robust fault detection of Markovian jump systems with different system modes

This paper deals with the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markovian jump systems with unknown input. By using a observer-based fault detection filter as residual generator, the RFDF design is formulated as an _H∞$H_{\infty }$-filtering problem. Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay. With the aid of the weighting matrix function, the design objective is to find an optimal RFDF, which results in a minimal difference between the reference model and the RFDF to be designed. By using a new convex polyhedron technique and two mode-dependent Lyapunov functional, some new sufficient conditions are established in terms of delay-dependent linear matrix inequalities (LMIs) to synthesize the residual generation scheme. Finally, a numerical example is given to illustrate the effectiveness of the proposed techniques.     

State feedback controller design for singular positive Markovian jump systems with partly known transition rates

The paper deals with the problem of state feedback controller design for singular positive Markovian jump systems with partly known transition rates. First, by applying an appropriate linear co-positive type Lyapunov–Krasovskii function, stochastic stability of the underlying systems is discussed. Based on the results obtained, a state feedback controller is constructed such that the closed-loop singular Markovian jump system is regular, impulse-free, positive and stochastically stable. All the provided conditions are based on a reliable computational approach in linear programming. Finally, an example is given to demonstrate the validity of the main results.     

A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates

This paper is devoted to investigating the problem of robust sliding mode control for a class of uncertain Markovian jump linear time-delay systems with generally uncertain transition rates (GUTRs). In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. A sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates. Finally, an example is presented to verify the validity of the proposed method.     

Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts

This paper addresses the problem of fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts. Both sensor-to-controller and controller-to-actuator packet dropouts are described by two different Bernoulli distributed white sequences, respectively. The problem addressed is to design an observer-based fault detection filter (FDF) such that the error between the residual and the fault is made as small as possible. Unlike most of the existing literature, we have noted that the control input of the observer is different from that of the plant because of packet dropouts in the controller-to-actuator link. Sufficient condition for the existence of the FDF is derived in terms of some linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the obtained results.     

Robust stability and stabilization of linear stochastic systems with Markovian switching and uncertain transition rates

This paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching. The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix. New criteria for testing the robust stability of such systems are established in terms of bi-linear matrix inequalities (BLMIs), and sufficient conditions are proposed for the design of robust state-feedback controllers. A numerical example is given to illustrate the effectiveness of our results.     

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H_∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H_∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H_∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.