Input-output Finite-time Stability Research Articles

Lower and upper bounds of the solution for the Lyapunov matrix differential equation and an application in input-output finite-time stability of linear systems

In control theory and practical engineering fields, such as the controllability, observability, input–output finite-time stability of the linear systems, it is a significant problem to study the properties of the solution for the Lyapunov matrix differential equation where there are no restrictions on the system matrix. In this paper, by constructing an equivalent form of the Lyapunov matrix differential equation and utilizing some important matrix eigenvalue inequalities, lower and upper bounds for the matrix solution of the Lyapunov matrix differential equation that remove the strict restrictions for the system matrix are proposed. As an application in linear systems, we show that our bounds can be used to discuss the input–output finite-time stability for linear systems. Finally, we give some corresponding numerical examples to illustrate the effectiveness and superiority of our results.

Imperfect premise matching finite-time filter design for continuous-time Takagi–Sugeno fuzzy systems

An input–output finite-time filtering design problem for a class of delayed Takagi–Sugeno fuzzy systems with external disturbance input is discussed in this paper. Specifically, the filter design uses the imperfect premise matching scheme that relaxes the requirement that the filter and system membership functions be the same. This method can improve the flexibility of the filter design by incorporating membership function information into the input–output finite-time stability analysis. Using the system and filter states, an augmented filtering system is obtained. The required stability criteria are then derived using the Lyapunov–Krasovskii stability theorem and a few recent inequality approaches. Following that, the desired filter gain matrices are determined. The developed filtering design method is validated through some demonstrative examples.

A Novel Asynchronous Sliding Mode Design for Switched Systems under Input–Output Finite-Time Stability

In this work, the input–output finite-time stability (IO-FTS) of a class of continuous-time switched systems characterized by uncertainties and subjected to external disturbances is studied under asynchronous switching by means of the sliding mode control (SMC) method. The IO-FTS poses a finite-time constraint problem, which involves addressing two main issues: firstly, ensuring that the state trajectory of the switched system reaches the given sliding mode surface within the specified time, and secondly, achieving IO-FTS for the closed-loop switched system during asynchronous switching. To address these issues, we apply a partitioning strategy and construct asynchronous sliding mode controllers with adjustable parameters to ensure the reachability of the system’s state trajectory within a finite time. Subsequently, we employ a multiple Lyapunov function (MLF) approach to provide sufficient conditions that ensure IO-FTS during the whole phase [0,T] for the resulting switched system. Additionally, we analyze the asynchronous characteristics concerning the reachability phase of the designed sliding surface, considering the system’s switching properties. Finally, we demonstrate the efficacy of the proposed approach with a numerical example.

Input–Output Finite-Time Stability for Switched T–S Fuzzy Delayed Systems With a Time-Dependent Lyapunov–Krasovskii Functional Approach

This research concerns the finite-time performance analysis for switched Takagi-Sugeno (T-S) fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input-output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input-output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input-output) finite-time analysis framework.

Input-output finite-time stabilization of periodic piecewise systems with multiple disturbances

In this work, the problems of input-output finite-time stability and disturbance rejection for continuous-time periodic piecewise systems with linear fractional uncertainty, matched and mismatched disturbances are investigated. In detail, the matched disturbances that are ensuing from the exogenous systems can be tackled by modeling a periodic piecewise disturbance observer (PPDO), which effectively estimates the disturbance with high precision. The mismatched part can be sorted out by implementing H∞ control protocol and meanwhile the state feedback is quantized in accordance with the logarithmic quantizer. On the whole, by combining the quantized state-feedback control law with the output of the PPDO, the anti-disturbance control protocol is developed. Moreover, by constructing a Lyapunov function with periodic piecewise positive definite matrices, a collection of adequate criteria affirming the system’s input-output finite-time stability are procured in the context of linear matrix inequalities (LMIs). Subsequently, the time-varying periodic piecewise gain values of the crafted disturbance observer and developed controller are acquired by working on the LMIs. Conclusively, the simulation results are provided, including the 2-degree of freedom vibration system, to verify the potential of the developed control strategy.

Input-Output Finite-Time Stability of Fractional-Order Switched Singular Systems with D-Perturbation

The objective of this paper focuses on the stability analysis of the input-output finite-time for a class of fractional-order switched singular systems (FOSSS) with D-perturbation. By using the Φ-dependent average dwell time (ΦDADT) approach together with the multiple Lyapunov functions method, some sufficient conditions are derived for the considered system to ensure its input-output finite-time stability in terms of linear matrix inequalities. Then, the output feedback controller is designed to ensure the closed-loop system is input-output finite-time stable. Finally, a numerical example illustrates the superiority of the proposed method.

Controller design of robot nonlinear system based on the improved fuzzy sliding mode control

In this paper, the input-output finite time stability of fuzzy sliding mode control in nonlinear robot systems is discussed. Specifically, the system considers more realistic factors, such as uncertainty, nonlinearity, interference, and state delay. An improved fuzzy sliding mode control (FSMC) scheme is developed, which is considered in most results of FSMC schemes. Based on the input-output finite-time stability characteristics and the proposed control scheme, the objective of this work is to reduce the effects of uncertainty, nonlinearity, disturbance, and state delay. Finally, the effectiveness and superiority of the proposed method are verified by simulation and comparison with other reference methods.

Finite-Time Bounded Tracking Control for a Class of Neutral Systems

In this paper, we investigate finite-time bounded (FTB) tracking control for a class of neutral systems. Firstly, the dynamic equation of the tracking error signal is given based on the original neutral system. Then, we combine it with the equations of the state vector to construct an error system, where the reference signal and the disturbance signal are fused in a new vector. Next, about the error system, we study the input–output finite-time stability problem of the closed-loop system by utilizing the Lyapunov–Krasovskii functional. We also give a finite-time stability condition in the form of linear matrix inequalities (LMIs). Furthermore, the delay-dependent and delay-independent finite-time bounded tracking controllers are designed separately for the original system. Finally, a realistic example is given to show the effectiveness of the controller design method in the paper.

Input-Output Finite-Time Sliding Mode Control of Discrete Time-Varying Systems Under an Adaptive Event-Triggered Mechanism

This paper is concerned with the issue of input-output finite-time stability (IO-FTS) for a class of nonlinear discrete time-varying systems. A time-varying observer-based sliding mode control method is proposed. In order to mitigate the transmission burden, an adaptive event-triggered mechanism is proposed by adjusting the threshold. Taking consideration of the effect of time-delay phenomenon and time-varying system matrices, a time-varying Lyapunov functional is designed. Based on the designed Lyapunov functional and IO-FTS theory, sufficient conditions are established for the error estimation system and closed-loop state estimation system. Moreover, the proposed observer-based sliding mode control method makes sure the reachability of the quasi-sliding mode surface in finite steps. And conditions in terms of recursive linear matrix inequalities (RLMIs) are attained to ensure IO-FTS during both reaching phase and sliding mode phase. An algorithm is provided to solve the RLMIs and obtain the time-varying observer gains. Finally, the effectiveness and superiority of the proposed method is demonstrated by an industrial continuous-stirred tank reactor system.

Proportional integral observer-based input–output finite-time stabilization for chaotic semi-Markov jump fuzzy systems

The goal of this article is to discuss the input–output finite-time (IO-FT) stabilization and state estimation problem for T-S fuzzy chaotic semi-Markov jump systems (TSFCS-MJSs) with uncertain transition rates, immeasurable states, quantization errors, gain fluctuations and external input signals by using quantized resilient proportional integral (PI) observer-based control. Precisely, to estimate the immeasurable states of the underlying TSFCS-MJSs, a mode-dependent fuzzy rule-based PI observer is implemented, wherein the inclusion of both proportional and integral loops provides more design freedom and finer steady-state accuracy. Additionally, the gain fluctuations that occur during the implementation of the addressed PI observer are taken into account and therefore, we focus on the design of resilient PI observer that provides satisfactory estimation results. Besides, by reason of the restricted capacity of the data transmission medium, the input signals are quantized prior to transmission. Following that, sufficient criteria are attained in the framework of linear matrix inequalities with the use of a mode-dependent Lyapunov function candidate can guarantee the resulting closed-loop system’s IO-FT stability. Thereafter, by solving the established linear matrix inequality-based criteria, the desired gain matrices of the controller and observer are computed. Finally, the simulation outcomes for standard Chua’s circuit system are displayed in accordance with the theoretical findings.

Constrained Reference Tracking via Structured Input–Output Finite-Time Stability

In this article, the control approach based on structured input–output finite-time stability (IO-FTS) is extended to tackle the reference tracking problem. IO-FTS was originally introduced to deal with the disturbance rejection problem. By applying the finite-time stability control to a properly augmented system, we show that it is possible to enforce a set of specific requirements on the response of the closed-loop system during the transients, taking also into account saturation constraints on the actuators. Adding IO-FTS constraints to classic-state-feedback control law leads to a feasibility problem with bilinear matrix inequality (BMI) constraints. Herein, we show how the original BMI problem can be relaxed to a linear matrix inequality (LMI) one, which comes at a price of more conservatism, but turns out to be computationally more efficient. To prove the effectiveness of the proposed approach, we consider the case of the longitudinal control of a missile.

Input-output finite-time stability of nonlinear descriptor systems

This article discusses the input-output finite-time stability and stabilization problems of a class of nonlinear descriptor systems. Two classes of disturbance inputs which belong to [Formula: see text] and [Formula: see text] are considered. Under the impulse-free condition of the descriptor systems, the article first studies the input-output finite-time stability with respect to the nonlinear descriptor systems with [Formula: see text] and [Formula: see text] disturbance inputs. Based on this, the design of the state feedback controllers ensures that the closed-loop descriptor systems are input-output finite-time stabilization. Finally, the results of simulation on a nonlinear descriptor circuit system verify the effectiveness of the controllers in this article.

Input–Output Finite-Time Stabilization of Linear Time-Varying Discrete-Time Systems

This article deals with the input–output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">finite</i> -interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example.

Input–Output Finite-Time Stabilization of T–S Fuzzy Systems Through Quantized Control Strategy

The issues of input–output finite-time stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and exogenous input signal are studied in this article. For the stabilization process, a controller that does not share the same membership functions as the system is considered and the state feedback is quantized by using a logarithmic quantizer. The desired stability criterion for the addressed fuzzy system is first derived without the control term. It is then extended to the case in which the proposed controller is present. The stability criteria are given in the form of matrix inequalities, which are supported by the augmented Lyapunov–Krasovskii functional, generalized free-weighting-matrix approach and Finsler’s lemma. Moreover, as a special case, an asymptotic stability criterion is obtained and used in a comparative study. As a result, the time-delay interval is much larger than some of the works published very recently, which is due to the augmented Lyapunov–Krasovskii functional construction. In addition, the effectiveness and practicability of the theoretical findings are validated with simulation examples.

Input–Output Finite-Time Asynchronous SMC for Nonlinear Semi-Markov Switching Systems With Application

This article investigates the input–output finite-time stability (IO-FTS) for nonlinear hidden semi-Markov switching systems (S-MSSs) via the asynchronous sliding mode control (SMC) approach. Under the assumption that a detector is set up to estimate the mode value, the mode of the original system is not directly accessible. The asynchrony between the system and controller is described as a hidden semi-Markov model (HSMM). Many practical factors, such as semi-Markov switching parameters, finite-time interval, asynchronous phenomenon, uncertain parameters, and nonlinearity, are taking into account during the SMC design process. We aim to design an efficient finite-time asynchronous SMC scheme under a hidden semi-Markov switching effect. A novel sliding switching surface (SSS) is constructed, in which the SMC law rises asynchronously with original S-MSSs. Then, by means of finite-time stability, an asynchronous SMC law is synthesized to guarantee that the associated hidden S-MSSs fulfill the reaching condition within a finite time. Furthermore, sufficient conditions are derived in view of the IO-FTS of sliding mode dynamics under the framework of a novel inequality lemma. Results are given for the application of this control design method to a single-link robot arm model (SLRAM).

Input-output finite-time control of Markov jump systems with round-robin protocol: An dynamic event-triggered approach

This article investigates the control problem of networked Markov jump systems (MJSs). First, to describe the asynchronization between the plant modes and the controller modes in MJSs, the hidden Markov model is introduced and the asynchronous control technique is developed. Next, the dynamic event-triggered mechanism (ETM) is utilized to decrease the frequency of data transmission. Moreover, the round-robin protocol (RRP) is introduced to reduce the amount of communicated data by allowing only one node to access the network. At last, the concept of input-output finite time stability (IO-FTS) is introduced and taken into consideration in the controller design. The highlight of this work is the introduction of both the dynamic ETM and the RRP to alleviate the communication load. Finally, a simulation example is proposed to illustrate the effectiveness of the theoretical results.

Multiple delay-dependent finite-time fault-tolerant control for switched fuzzy systems

The work is concerned with this issue of multiple delay-dependent finite-time fault-tolerant control (FTC) for uncertain switched Takagi-Sugeno (T-S) fuzzy systems against state and input constraints. There exist intermittent faults (IFs), exogenous disturbances along with measurement noise in the models. There are few attempts for this theme. A nonlinear dynamic output feedback controller is explored for these uncertain switched T-S fuzzy systems first. And an augmented system with respect to realizing FTC is acquired. Moreover, sufficient conditions of robust finite-time H∞ control are constructed by piecewise fuzzy Lyapunov function. At the same time, finite-time boundedness (FTB) as well as input-output finite-time stability (IO-FTS) is achieved. The effectiveness as well as feasibility of this approach is verified through an example.

Combined Input–Output Finite-time Stability with H∞ Static Output-feedback Control Approach for Active Suspension

Combined input–output finite-time stability condition with static output-feedback H ∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H ∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H ∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

Input–Output Finite-Time Sliding-Mode Control for T–S Fuzzy Systems With Application

This article addresses the issue of input-output finite-time stability (IO-FTS) for nonlinear systems by employing sliding-mode control (SMC) methodology. Many practical systems subject to complex factors, such as the single-link robot arm model (SLRAM), can be characterized as nonlinear systems. Our attention is focused on designing a fuzzy-model-based finite-time SMC law to attenuate the influences of uncertainty, nonlinear term, and external disturbance during the finite-time region. First, a novel integral sliding-mode surface is proposed based on the Takagi-Sugeno fuzzy rule. Then, by using the key point of Lyapunov function theory, an appropriate fuzzy SMC law is designed to make sure that the signal variables can arrive at a domain within the assigned fixed-time level. Moreover, some new IO-FTS criteria are constructed for the resulting sliding dynamics over the whole finite-time level, including reaching phase and sliding motion phase. Via the SLRAM, we demonstrate the effectiveness of the proposed SMC approach.

Robust finite-Time control and reachable set estimation for uncertain switched neutral systems with time delays and input constraints

This work focuses on robust finite-time fault-tolerant control and reachable set estimation for uncertain switched neutral systems subject to time delays as well as input constraints. There are few attempts to investigate robust finite-time boundedness and reachable set estimation for uncertain switched neutral systems. At the same time, input-output finite-time stability is also investigated. Compared with the existing studies, this system has wider application. A dynamic output feedback nonlinear controller is researched. An augmented closed-loop system is provided. Moreover, the sufficient conditions of finite-time boundedness, reachable set estimation and input-output finite-time stability for the closed-loop system are obtained in the framework of linear matrix inequalities via piecewise Lyapunov function. Ultimately, two examples are provided to demonstrate this validity of this approach in this paper.