Finite-time Boundedness Research Articles

Finite-time Boundedness of Polytopic Uncertain Systems with Guaranteed Cost Output Feedback Control

A problem of designing robust guaranteed cost reduced-order output feedback controllers for finite-time boundedness of linear time-varying uncertain systems is considered in this paper. Assuming the system parameters to lie in a polytopic set, differential linear matrix inequality (DLMI) conditions for the design of reduced-order dynamic controllers to handle worst-case exogenous disturbances are derived. The designed controller guarantees the cost on considered disturbance attenuation performance on the system to be below an upper bound, while simultaneously satisfying the conditions for finite-time boundedness and finite L2 gain. Numerical simulations are carried out to demonstrate the applicability of the proposed method in bounding the system trajectories to a predefined set.

Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time Method.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

Distributed Finite-Time Boundedness Control for Large-Scale Networked Dynamic Systems

Distributed Finite-Time Boundedness Control for Large-Scale Networked Dynamic Systems

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

<abstract><p>This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.</p></abstract>

Reduced-Order Min-Max Guaranteed Cost Control for Finite-Time Boundedness of Uncertain Linear Systems Using Output Feedback

This letter considers a problem of designing reduced-order dynamic output feedback controllers for finite-time boundedness of uncertain linear time-varying systems subjected to exogenous disturbances. Differential linear matrix inequality conditions are derived for finite-time boundedness with output feedback, such that the uncertain system simultaneously satisfies finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {L}_{2}$ </tex-math></inline-formula> gain in the presence of worst-case exogenous disturbances. The designed min-max controller minimizes an upper bound on the considered performance index, providing a guaranteed cost for disturbance attenuation performance. Finite-time bounded state feedback controller design is shown to be a special case of the proposed method. The performance efficacy and applicability of the controller designed using the proposed iterative algorithm are compared with some of the recent methods from the literature.

Finite-time stability of set switched systems with non-instantaneous impulses

In this paper, we discuss the finite-time stability of set switched systems with non-instantaneous impulses which consist of stable and unstable subsystems through introducing a revised mode-dependent average dwell time method. By designing time-dependent switching law and using the multiple Lyapunov-like functions method, the finite-time stability criteria of set switched systems with non-instantaneous impulses are given. Sufficient conditions which guarantee the finite-time boundedness of the switched systems with time-varying exogenous disturbances are also given. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. The criteria obtained for the switched linear systems are all provided in terms of a set of linear matrix inequalities. Numerical examples are employed to verify the efficiency of the proposed method.

Finite-time boundedness of networked control systems via hybrid predictive control based on cloud storage method

In this paper, we investigate the problem of predictive control for a class of networked control systems (NCSs) based on the cloud storage method (CSM). To improve the system’s transient performance and actively compensate for the time-varying delays (TVDs) and data packet dropouts (DPDs), a hybrid networked predictive control (NPC) method is proposed. The switched control system is established based on a class of switching signals varying with the TVDs and DPDs. Novel finite-time hybrid stabilization controllers are proposed by using NPC theory. Then, sufficient conditions are developed to ensure the finite-time boundedness (FTB) of the augmented switched systems. Two experiments illustrate the performance to verify the effectiveness of the proposed results.

Finite-Time sliding mode control for singularly perturbed PDE systems

This article proposes a sliding mode control strategy for hyperbolic PDE systems under the requirement of finite-time boundedness. First, the singular perturbation theory is introduced to model multi-time scales phenomena, and a quantized measurement method is employed to save the communication resources in network. In addition, by considering the effect of the singular perturbation phenomenon in PDE systems, a sliding surface dependent on spatial position and singular perturbation parameter is constructed, then a sliding mode control law is developed to drive state trajectories to the designed sliding surface in finite time. Moreover, a partitioning strategy is introduced to ensure that the system is finite-time bounded in the reaching phase and the sliding motion phase, respectively. Finally, some sufficient conditions are given to ensure that the system is finite-time bounded in both reaching phase and sliding motion phase, and a simulation example of the chemical tubular reactor demonstrates the effectiveness of the proposed method.

Event-triggered annular finite-time [formula omitted] filtering for stochastic network systems

The event-triggered annular finite-time H∞ filtering problem is addressed for stochastic network systems in this paper. The influence of stochastic disturbance is considered in the whole framework of filter design. A zero-order-holder (ZOH) is introduced to maintain and send the delayed output signals for filter updating. By resorting to a novel delay-dependent Lyapunov-Krasovskii functional (LKF) and LMI technique, the stochastic annular finite-time boundedness of the filtering error system is analyzed. Furthermore, the H∞ filter design under the event-triggered mechanism is established in the sense of a prescribed H∞ performance level. Finally, two numerical examples are realized to illustrate the validity of the proposed results.

Finite-Time Composite Antidisturbance Control for T–S Fuzzy Nonhomogeneous Markovian Jump Systems via Asynchronous Disturbance Observer

This article studies the finite-time composite antidisturbance control problem for nonhomogeneous Markovian jump systems (MJSs) subject to multiple disturbances via the Takagi–Sugeno (T–S) fuzzy control scheme. The designed two-gains disturbance observer (DO) and the considered MJSs are supposed to switch the different Markovian chains, which are depicted by a hidden Markovian model. Herein, an asynchronous DO design is explored for the first time, providing new insight into the construction of asynchronous DO. First, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty /L_{2}-L_\infty$</tex-math></inline-formula> finite-time boundedness of the augmented system is guaranteed. Second, based on the Finsler lemma, the linearization issue in calculating observer/controller gain is addressed. Finally, two illustrations are presented to verify the effectiveness of the proposed method.

Protocol-Based Control for Semi-Markov Jump Systems With Dynamic Quantization

This brief is devoted to protocol-based control method design for semi-Markov switching systems with dynamic quantization. Essential different from the semi-Markov process with arbitrary switchings, by proposing a novel semi-Markov process subjected to a deterministic switching signal, a generalized framework of semi-Markov switching systems is set up. With respect to the quantization range of the dynamic quantizer, an improved event-triggered protocol associated with the quantizer parameter is proposed. On account of mode-dependent Lyapunov theory, sufficient conditions are established to ensure the stochastic finite-time boundedness of the resulting system. In the end, a tunnel diode circuit model shows the practicability and effectiveness of the presented method.

Finite-time H∞ control of discrete-time switched systems based on transferring-dependent Lyapunov function approach

This paper studies the finite-time issues (finite-time stability, finite-time boundedness, finite-time [Formula: see text] control) of discrete-time switched systems. Different from the existing Lyapunov function (LF) approaches only concerning activated subsystem, a novel approach for constructing LF is first proposed, which not only depends on the subsystem the switching reaches but also is closely related to the freshly inactive subsystem. Based on this, a transferring-dependent convex Lyapunov function (CLF) and a transferring-dependent LF are introduced, under which the improved finite-time stability results are deduced with admissible edge-dependent average dwell time (AED-ADT) technique. In light of the merits of established finite-time stability criteria, two transferring-dependent controllers are devised—that is, transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC)—to perform finite-time control synthesis. Then, the finite-time [Formula: see text] control is further investigated based on the obtained control synthesis results. The designed transferring–dependent controllers can guarantee that the underlying system is finite-time bounded (FTB) with a prescribed [Formula: see text] performance under tighter AED-ADT switching signals. Besides, it is the first time to use the multiple convex Lyapunov function (MCLF) to investigate the finite-time issues. Finally, two numerical examples and a practical example are used to verify the effectiveness of the developed results.

State estimation-based robust control design for periodic piecewise systems with time-varying delays

In this article, the issue of finite-time boundedness is investigated for a class of uncertain periodic piecewise systems subject to time-varying input/state delays and external disturbances. The main aim of this article is to design an observer-based control protocol for guaranteeing the resulting closed-loop system to be finite-time bounded. The state dynamics of the system are not always directly measurable, so that a system states are reconstructed by constructing a periodic piecewise observer system to get the required result. Subsequently, the Lyapunov–Krasovskii functional by the decomposition of periodic positive-definite matrices is built and in conjunction with convex optimisation technique and extended Wirtinger's integral inequality, the sufficient conditions are derived to assure the finite-time boundedness of the closed-loop system. In particular, the corresponding periodic piecewise time-varying controller and observer gain matrices can be obtained as solutions to a set of derived sufficient linear matrix inequality-based conditions. Finally, the efficacy of the proposed control design is examined by utilizing two numerical examples with simulation results including a vibration system model.

Admissible edge-dependent finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time

Considering that the property of finite-time convergence is of great significance for practical filters, this article is focused on the finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time. Different from the case of the general mode-dependent switching, the information of the admissible switching edge is fully exploited to derive more preferable filtering scheme. In order to further reduce the design conservatism, the multiple discontinuous Lyapunov function approach, which incorporates the concept of admissible edge-dependent average dwell time, is used to analyze the finite-time stability and ℋ∞ performance of the filtering error system. This approach assigns each subsystem of the error system with a discontinuous function rather than a continuous one, so it is less conservative compared to the conventional multiple Lyapunov function approach. First, the finite-time boundedness and ℋ∞ performance is analyzed for general switched nonlinear systems with admissible edge-dependent average dwell time. Then, a sufficient condition of the finite-time boundedness and ℋ∞ performance is derived for the filtering error system based on the obtained criterion. Subsequently, an admissible edge-dependent finite-time filtering scheme is proposed for the underlying system in terms of linear matrix inequalities. Finally, the proposed filter design scheme is applied to a DC–DC power converter circuit, and its effectiveness and superiority are verified by the simulation results.

New Approach to Observer-Based Finite-Time H∞ Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

This paper investigates the finite-time H∞ control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties. Using the one-sided Lipschitz and quadratically inner-bounded conditions, the authors derive less conservative criterion for the controller design and observer design. A new criterion is proposed to ensure the closedloop system is finite-time bounded (FTB). The sufficient conditions are established to ensure the closed-loop system is H∞ finite-time bounded (H∞ FTB) in terms of matrix inequalities. The controller gains and observer gains are given. A numerical example is provided to demonstrate the effectiveness of the proposed results.

Adaptive Event-Triggered Finite-Time Dissipative Filtering for Interval Type-2 Fuzzy Markov Jump Systems With Asynchronous Modes.

This article investigates the adaptive event-triggered finite-time dissipative filtering problems for the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy Markov jump systems (MJSs) with asynchronous modes. By designing a generalized performance index, the H∞ , L2-L∞ , and dissipative fuzzy filtering problems with network transmission delay are addressed. The adaptive event-triggered scheme (ETS) is proposed to guarantee that the IT2 T-S fuzzy MJSs are finite-time boundedness (FTB) and, thus, lower the energy consumption of communication while ensuring the performance of the system with extended dissipativity. Different from the conventional triggering mechanism, in this article, the parameters of the triggering function are based on an adaptive law, which is obtained online rather than as a predefined constant. Besides, the asynchronous phenomenon between the plant and the filter is considered, which is described by a hidden Markov model (HMM). Finally, two examples are presented to show the availability of the proposed algorithms.

Almost Sure Finite-Time Control for Markovian Jump Systems Under Asynchronous Switching With Applications: A Sliding Mode Approach

The almost sure finite-time sliding mode control issue is investigated for Markov jump systems. The switching asynchronism between the constructed controller and considered systems is studied. The influence of time-varying delays and disturbances on systems is fully considered, and the sliding mode controller design within a finite time interval is extended to the probability framework. First, the finite time interval is divided into the reaching and the sliding motion phases, and the almost sure finite-time boundedness is analyzed in both phases. Second, the sliding mode controller gain is determined by the provided linear matrix inequality-based criteria. Finally, a numerical example and DC-DC buck converter circuit example verify the effectiveness and less conservativeness of our method.

Finite-time mixed [formula omitted] and passivity analysis for Takagi–Sugeno fuzzy system with time-varying delays and actuator faults

This paper comes up with an novel augmented Lyapunov–Krasovskii functional (LKF) approach to process finite-time passivity-based H∞ non-fragile state feedback control issue of Takagi–Sugeno fuzzy system (TSFS) via taking the effects of both time-varying delays and actuator faults. Designing a non-fragile controller to guarantee that TSFS is finite-time bounded (FTB) and meet finite-time mixed H∞ and passive performance is the focus of this paper. On the basis of the new augmented LKF and improved boundary techniques, sufficient delay-dependent conditions are inferred to acquire the desired results of the TSFS. Furthermore, the derived finite-time stability conditions are derived in terms of linear matrix inequalities (LMIs) and the controller gain matrices are confirmed through solving LMIs. Subsequently, three examples are addressed to certify the applicability and advantage of the put forward methodology.

A Hierarchical Structure Approach to Finite-Time Filter Design for Fuzzy Markov Switching Systems With Deception Attacks.

This work is concerned with the issue of finite-time filter design for a type of Takagi-Sugeno (T-S) fuzzy Markov switching system (MSSs) with deception attacks (DAs). In view of communication network security, the randomly occurring DAs are considered in the measurement output (MO), in which the malicious unknown but bounded signals are launched by the adversary. Notably, to characterize the fallibility of the communication links between the MO and the filter, the packet dropouts, DAs, and quantization effects are taken into account simultaneously, which signifies that the resulting system is much more applicable than the existing results. Meanwhile, to deal with the phenomenon of asynchronous switching, a hierarchical structure approach is adopted, which involves the existing nonsynchronous/synchronous strategy as special cases. By means of a fuzzy-basis-dependent Lyapunov strategy, sufficient criteria are formulated such that the resulting system is stochastic finite-time boundedness under randomly occurring DAs. Finally, a double-inverted pendulum model and a numerical example are provided to validate the feasibility of the attained method.

Finite-time dissipative control for bidirectional associative memory neural networks with state-dependent switching and time-varying delays

This paper focuses on finite-time exponential dissipative analysis and control problems for bidirectional associative memory neural networks (BAMNNs) with state-dependent switching and time-varying delays. Firstly, the state-dependent switching parameters of BAMNNs are interpreted as interval parameters by the interval matrix method instead of differential inclusion theory and set-value map. Under the framework of Filippov’s solution and differential inclusions, some sufficient conditions of finite-time bounded (FTB) and finite-time exponential (Q,S,R)−γ dissipative (FTED) for BAMNNs are obtained based on Lyapunov–Krasovskii functional (LKF) and some inequality techniques. Then, the finite-time dissipative PI controllers are designed by solving linear matrix inequality (LMI). Finally, a numerical example is given to illustrate the correctness of the proposed results and the effectiveness of the designed controllers.