Input-output Finite-time Stabilization Research Articles

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

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.

Event-Triggered Input–Output Finite-Time Stabilization for IT2 Fuzzy Systems Under Deception Attacks

This article addresses the issue of input–output finite-time stabilization for interval type-2 fuzzy systems in the presence of deception attack effects. Our main goal is to make efficient use of network resources by developing an event-triggered controller for interval type-2 fuzzy systems. For the stabilization process, an event-triggered controller that does not share the same membership functions as the system is designed by using affine transformation parameters. Following that, by using an asymmetric Lyapunov–Krasovskii functional and some advanced integral inequalities to establish the sufficient conditions for the existence of the proposed controller. Furthermore, an asymptotic stabilization result is presented and discussed in a comparative analysis as a special case. Due to the asymmetric Lyapunov–Krasovskii functional structure, the transmission delay interval is large compared with some recent studies. Finally, two simulation examples are carried out and the efficiency of designed controller is verified.

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.

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.

Multiple delay-dependent event-triggered finite-time [formula omitted] filtering for uncertain networked random systems against state and input constraints

In this article, multiple delay-dependent event-triggered finite-time H∞ filtering as well as fault-tolerant control is discussed for networked random systems subject to state as well as input constraints. This is the first time to explore fault detection issue via filtering for networked random models. First, an event-triggered scheme is designed. Secondly, a zero order holder is studied. According to this event-triggered mechanism, a fault detection filter, a fault weighting system and a controller are investigated for the networked random system. And then an augmented system can be got. Sufficient conditions of mean-square finite-time boundedness with input-output finite-time mean square stabilization can be provided through the framework of linear matrix inequalities. Finally, these effectiveness and merits are verified by an example.

Dissipativity-Based Finite-Time Filtering for Uncertain Semi-Markovian Jump Random Systems With Multiple Time Delays and State Constraints

This article is concerned with the issue of dissipativity-based finite-time multiple delay-dependent filtering for uncertain semi-Markovian jump random nonlinear systems with state constraints. There are multiple time-varying delays, nonlinear functions, and intermittent faults (IFs) in the systems. This is one of the few attempts for the issue studied in this article. First, a filter is designed for the uncertain semi-Markovian jump random nonlinear systems. An augmented system with regard to the resulting filtering error is acquired. Then, sufficient conditions of the augmented system are generated by the stochastic Lyapunov function. Finite-time boundedness (FTB) and input-output finite-time mean square stabilization (IO-FTMSS) are both realized. The effectiveness and feasibility of the method are rendered via three examples.

Multiple delay-dependent finite-time boundedness and input–output finite-time mean square stabilization of uncertain semi-Markovian jump systems with input constraint

This study is concerned with the problem of finite-time fault-tolerant control for uncertain semi-Markovian jump systems with input constraint and multiple time delays. There exist nonlinear functions, exogenous disturbances and measurement noise in these nonlinear systems. First, a dynamic output feedback controller is constructed for the uncertain semi-Markovian jump systems. A closed-loop system is earned. Next, sufficient stability conditions of the closed-loop system are obtained via stochastic Lyapunov function. Not only finite-time boundedness but also input-output finite-time mean square stabilization is achieved. This study is the first time to study. Finally, an example is provided to prove the novelty of the approach proposed in this paper.

Input–output finite-time stabilization for MJSs with time-varying delay: An observer-based approach

This paper deals with the input–output finite-time stabilization problem for Markovian jump systems (MJSs) with incompletely known transition rates. An observer-based output feedback controller is constructed to study the input–output finite-time stability (IO-FTS) problem. By using the mode-dependent Lyapunov–krasovskii functional method, a sufficient criterion checking the IO-FTS problem is provided. Then, an observer and a corresponding state feedback controller for the individual subsystem are respectively designed to solve the input–output finite-time stabilization problem for the systems. Finally, a numerical example on the mass-spring system model is investigated to bring out the advantages of the control scheme proposed in this paper.

Input–output stabilization-based finite-time robust control of disturbed systems using linear matrix inequality approach

In this paper, finite-time robust control problems are considered for a class of uncertain systems subject to exogenous disturbances, and an input–output finite-time stabilization (IO-FTS) method is presented with finite-time boundedness (FTB) constraints. For an uncertain system, a state feedback controller is designed, via linear matrix inequalities (LMIs), to ensure the IO-FTS and FTB of the closed-loop system. By using Lyapunov stability theory, sufficient conditions for IO-FTS and FTB are given. These conditions are expressed as a feasibility problem of a set of LMIs. The direct current motor control problem and roll autopilot design of a skid-to-turn missile are considered for a case study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach to controlling similar uncertain systems.

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

Time-varying impulsive positive hybrid systems based on finite state machines (FSMs) are considered in this paper, and the concept of input–output finite time stability (IO-FTS) is extended for this type of hybrid system. The IO-FTS analysis of the single linear time-varying system is given first. Then, the sufficient conditions of IO-FTS for hybrid systems are proposed via the mode-dependent average dwell time (MDADT) technique. Moreover, the output feedback controller which can stabilize the non-autonomous hybrid systems is derived, and the obtained results are presented in a linear programming form. Finally, a numerical example is provided to show the theoretical results.

Input–output finite-time stabilization of a class of nonlinear hybrid systems based on FSM with MDADT

This thesis investigates the problem of input–output finite-time stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM). First, the concept of input–output finite-time stability (IO-FTS) is extended for such hybrid systems, then, the stability analysis is given by combining the multiple Lyapunov functions (MLFs) method and mode-dependent average dwell time (MDADT) technique, the corresponding sufficient conditions are derived and proved. Furthermore, a state feedback controller is designed to stabilize the hybrid systems. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed controller.

Input–output finite-time stabilization of Markovian jump systems with convex polytopic switching probabilities

In this paper, the problem of input–output finite-time stabilization of Markovian jump systems with convex polytopic switching probabilities is addressed. First, a new criterion for testing the input–output finite-time stabilization of such systems is established. Then, in terms of linear matrix inequalities, a sufficient condition is proposed for the design of robust state-feedback controllers. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.

Triangle Interception Scenario: A Finite-Time Guidance Approach

Considering an aircraft threatened by an interceptor, one of the effective penetration strategies is to release a Defender from the aircraft to confront the interceptor. In this case, the aircraft, the Defender, and the interceptor constitute the three-body guidance relationship, and the cooperation of the aircraft and its Defender to achieve the best tactical effects turns into a concerned problem. This paper studies the triangle interception guidance problem via the finite-time theory. The paper presents linear system Input-Output Finite-Time Stabilization (IO-FTS) method. The sufficient conditions of the linear system, being IO-FTS, under Finite-Time Boundedness (FTB) constraint are proposed, by which the state feedback controllers design method is obtained, via Linear Matrix Inequalities (LMIs). The triangle interception guidance problems are studied in three different cases, where the proposed methods are applied to the guidance design. The simulation results illustrate the effectiveness of the proposed methods.

Finite-time sliding mode control synthesis under explicit output constraint

This work deals with the input–output finite-time stabilization problem for a class of nonlinear systems by employing sliding mode control (SMC) approach. A suitable SMC law is designed to ensure that the state trajectories can be driven onto the specified sliding surface during the assigned finite-time interval. Moreover, some parameters-dependent sufficient conditions are derived such that the input–output finite-time stability (IO-FTS) during both reaching phase and sliding motion phase are attained. Simulation results are provided to illustrate the proposed approach.

Input–output finite-time stabilization of impulsive linear systems: Necessary and sufficient conditions

The main result of this paper consists of a pair of necessary and sufficient conditions for the input–output finite-time stability of impulsive linear systems. The former requires that an optimization problem, constrained by a coupled differential/difference linear matrix inequality (LMI), admits a feasible solution; the latter that the solution of a coupled differential/difference Lyapunov equation satisfies a constraint on the maximum eigenvalue. The first condition was already provided in Amato et al. (2011), where, however, only sufficiency was proven. The novel analysis condition (i.e. the one requiring the solution of the differential/difference Lyapunov equation) is shown to be more efficient from the computational point of view, while the result based on the differential/difference LMI is the starting point for the derivation of the design theorem. Some examples illustrate the benefits of the proposed technique.

Input–output finite-time stabilization of linear systems with finite-time boundedness

The paper presents linear system Input–Output Finite-Time Stabilization (IO-FTS) method under Finite-Time Boundedness (FTB) constraint. A state feedback controller is designed, via Linear Matrix Inequalities (LMIs), to guarantee the system both IO-FTS and FTB. The proposed methods are applied to the guidance design of a class of terminal guidance systems to suppress disturbances with IO-FTS method and FTB constraints simultaneously satisfied. The simulation results illustrate the effectiveness of the proposed methods.

Input–Output Finite-Time Stability of Linear Systems: Necessary and Sufficient Conditions

In the recent paper “Input-output finite-time stabilization of linear systems,” (F. Amato ) a sufficient condition for input-output finite-time stability (IO-FTS), when the inputs of the system are <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> signals, has been provided; such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). Roughly speaking, a system is said to be input-output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , the outputs of the system do not exceed an assigned threshold during such time interval. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. In this context, this paper presents several novel contributions. First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. Amato is actually also a necessary condition for IO-FTS; at the same time we provide an alternative-still necessary and sufficient-condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). We show that the last condition is computationally more efficient; however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples; in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.