Input–output finite-time stabilisation of nonlinear stochastic system with missing measurements

This paper considers the problem of the input–output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input–output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.     

Input–output finite-time stability of discrete-time systems under finite-time boundedness

This paper deals with the input–output finite-time stability of discrete time-varying linear systems in the presence of finite-time boundedness. The state boundedness and output stability of this system are concerned simultaneously to avoid the large unacceptable values during certain transients. For two different classes of norm-bounded input signals, the sufficient conditions for the system satisfying both the state finite-time boundedness (FTB) and input–output finite-time stability (IO-FTS) are developed. Based on a set of linear matrix inequalities (LMIs), the controller design method via state feedback for the discrete-time system satisfying both FTB and IO-FTS is presented for the two classes of external norm-bounded input. The conditions proposed can simultaneously guarantee the state and output of closed-loop system do not exceed the boundary during the specified finite-time interval. Two examples are employed to verify the effectiveness of the proposed method.     

Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

This article investigates the problem of robust ?_∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ?_∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ?_∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov–Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.     

Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays

In this paper, robust H_∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.     

Stabilization of stochastic systems with hidden Markovian jumps

This paper considers the adaptive control of discrete-time hybrid stochastic systems with unknown randomly jumping parameters described by a finite-state hidden Markov chain. An intuitive yet longstanding conjecture in this area is that such hybrid systems can be adaptively stabilized whenever the rate of transition of the hidden Markov chain is small enough. This paper provides a rigorous positive answer to this conjecture by establishing the global stability of a gradient-algorithm-based adaptive linear-quadratic control.     

Stabilisation and H∞ control of neutral stochastic delay Markovian jump systems

This paper investigates the exponential stabilisation and H_∞ control problem of neutral stochastic delay Markovian jump systems. First, a delay feedback controller is designed to stabilise the neutral stochastic delay Markovian jump system in the drift part. Second, sufficient conditions for the existence of feedback controller are proposed to ensure that the resulting closed-loop system is exponentially stable in mean square and satisfies a prescribed H_∞ performance level. Finally, numerical examples are provided to show the effectiveness of the proposed design methods.     

Robust H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It^o stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.     

Delay-range-dependent robust stabilisation and H ∞ control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays and Markovian jump parameters

This article focuses on the problems of robust stabilisation and H _∞ control for nonlinear uncertain stochastic systems with mode-dependent time delay and Markovian jump parameters represented by the Takagi–Sugeno (T-S) fuzzy model approach. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbances, Markovian jump parameters and unknown nonlinear disturbances. The purpose is to design a state feedback controller such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H _∞ performance level. Novel delay-range-dependent conditions in the form of linear matrix inequalities (LMIs) are derived for the solvability of robust stabilisation and H _∞ control problem. A desired fuzzy controller can be constructed by solving a set solutions of LMIs and can be easily calculated by Matlab LMI control toolbox. Finally, a numerical example is presented to illustrate the proposed method.     

Input–output decoupling by output feedback with disturbance attenuation of H∞ control for any square system

The combined problem of diagonal decoupling by output feedback with disturbance attenuation performance for any square system is formulated. A sufficient condition which is more general than the necessary and sufficient one of static state feedback for the existence of the controller is determined. The necessary and sufficient conditions for the controller and decoupled system that are both stable are presented. An analytical form and a numerical computable method for the controller are obtained for the first time when the condition is satisfied. The correctness of our method is tested by simulations for an example.     

Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

This paper investigates the problem of reliable finite-time H_∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H_∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.     

H ∞ output feedback stabilisation of linear discrete-time systems with impulses

This article addresses the issue of designing an H _∞ output feedback controller for linear discrete-time systems with impulses. First, a new concept of H _∞ output feedback stabilisation for general linear discrete-time systems with impulses is introduced. Then sufficient linear matrix inequality conditions for the stabilisation and H _∞ performance of general discrete systems with impulses are proposed. In addition, the result is applied to resolve typical output feedback control problems for systems with impulses, such as the decentralised H _∞ output feedback control and the simultaneous H _∞ output feedback control. Finally, a numerical simulation is also presented to illustrate the effectiveness of the proposed results.     

Security control of positive semi‑Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourntime distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.     

Input–output operability of control systems: The steady-state case

For high-dimensional systems with more outputs than inputs, some outputs must be controlled within ranges, instead of at set-points. This may also be true if the outputs are equal in number to the inputs and disturbances of high magnitude exist. A linear programming framework is postulated to calculate the tightest achievable operating ranges of the outputs, given the ranges of the inputs and the expected disturbances, for any linear input–output control system at the steady-state. This approach removes the computational constraints on the size of the problem that a previous communication of the authors [1] could address. The hyper-volume obtained for the tightest achievable outputs’ region of a high-dimensional industrial process is calculated to be four orders of magnitude smaller than the one initially assumed, enabling much tighter control.     

H∞ fuzzy control of semi-Markov jump nonlinear systems under σ-error mean square stability

This paper is concerned with the problem of time-varying H_∞ fuzzy control for a class of semi-Markov jump nonlinear systems in the sense of σ-error mean square stability. The nonlinear plant is described via the Takagi–Sugeno fuzzy model. By defining a time-varying mode-dependent Lyapunov function, a set of sufficient stability and stabilisation criteria for non-disturbance case is first derived and then applied to the investigation of H_∞ performance analysis and H_∞ fuzzy controller design problems of semi-Markov jump nonlinear systems. Different from the traditional stochastic switching system framework, the probability density function of sojourn time is exploited to circumvent the complex computation of transition probabilities. The derived conditions can cover the time-invariant mode-dependent and time-invariant mode-independent H_∞ fuzzy control schemes as special cases. A classic cart-pendulum system is presented to demonstrate the effectiveness and advantages of the proposed theoretical results.     

Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays

This article investigates the problems of H _∞ analysis for Markovian jump stochastic systems with both nonlinear disturbance and time-varying delays. By virtue of the delay partition approach, the improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump stochastic systems are obtained in terms of linear matrix inequalities (LMIs). The proposed approach involves neither free weighting matrices nor any model transformation, and it is shown that the new criteria have the capability of providing less conservative results than the state-of-the-art. Two numerical simulations are conducted to demonstrate the effectiveness of the proposed method in comparison with existing methods.     

Stability and stabilisation of Itô stochastic systems with piecewise homogeneous Markov jumps

This paper focuses on the problem of stability and stabilisation for continuous-time Itô stochastic Markovian jump linear systems with time-varying transition rates. The time-varying property of the transition rates is considered to be finite piecewise homogeneous. Firstly, the stability conditions of the piecewise homogeneous Itô stochastic Markovian jump linear systems are given in terms of linear matrix inequalities (LMIs). Especially, a novel stability criterion is developed for the considered systems by the existence of the unique positive-definite solution of the corresponding coupled Lyapunov matrix equations. Secondly, two state-feedback controllers are designed via LMIs to stabilise the systems. Finally, a practical example is provided to illustrate the effectiveness of the presented theoretical results.     

Robust fault detection for discrete-time Markovian jump systems with mode-dependent time-delays

This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual generator based on the filter of which its parameters matrices are dependent on the system mode, that is, the fault detection filter is a Markovian jump system as well. The design of fault detection filter is reduced to H-infinity filtering problem by using H-infinity control theory, which can guarantee the difference between the residual and the fault (or, more generally weighted fault) as small as possible in the context of enhancing the robustness of residual to modeling errors, control inputs and unknown inputs. Sufficient condition for the existence of the above filters is established by means of linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the feasibility of the proposed method.