Xiaomeng Shi

Bio: Xiaomeng Shi is an academic researcher from Tianjin University. The author has contributed to research in topics: Dwell time & Exponential stability. The author has an hindex of 5, co-authored 5 publications receiving 146 citations.

On finite-time stability for nonlinear impulsive switched systems

Abstract: This paper is concerned with the finite-time stability problem for switched systems subject to both nonlinear perturbation and impulse effects. The average dwell time approach, combined with the algebraic matrix theory, is utilized to derive a criterion guaranteeing that the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval. The requirement that at least one subsystem should be stable to ensure asymptotic stability is no longer necessary. Moreover, the finite-time stability degree could be positive, which is a relaxed condition for asymptotic stability. A numerical example is presented to illustrate the effectiveness of the proposed method.

Average dwell time approach to finite-time stabilization of switched singular linear systems

Abstract: This paper is concerned with the finite-time stabilization problem for a class of switched singular linear systems. The dynamic decomposition technique is utilized to convert such a problem to an equivalent one for the reduced-order switched normal system with state jumps. The average dwell time approach is proposed which ensures the system׳s state trajectory remaining in a bounded region of the state space over a pre-specified finite-time interval. To further reduce the conservatism, the mode-dependent average dwell time method is adopted. Finally, two numerical examples are given to show the validity and potential of the developed methods.

Finite-Time Stability Analysis of Impulsive Switched Discrete-Time Linear Systems: The Average Dwell Time Approach

Abstract: This paper investigates the finite-time stability problem for a class of discrete-time switched linear systems with impulse effects. Based on the average dwell time approach, a sufficient condition is established which ensures that the state trajectory of the system remains in a bounded region of the state space over a pre-specified finite time interval. Different from the traditional condition for asymptotic stability of switched systems, it is shown that the total activation time of unstable subsystems can be greater than that of stable subsystems. Moreover, the finite-time stability degree can also be greater than one. Two examples are given to illustrate the merit of the proposed method.

Finite-time stability for continuous-time switched systems in the presence of impulse effects

Abstract: The problem of finite-time stability for a class of continuous-time switched systems with impulse effects is studied in this article. A criterion is proposed which ensures that the system’s state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if the authors give a bound on the initial condition. Contrary to the existing results on finite-time stability of switched systems, the average dwell time approach, rather than the Lyapunov-based ones, is utilised to realise such a purpose. The difference between the finite-time stability and the Lyapunov stability is clearly shown. A numerical example is given to illustrate the proposed design method.

Finite-time stability analysis of impulsive discrete-time switched systems with nonlinear perturbation

Abstract: The problem of finite-time stability for a class of discrete-time switched systems in the presence of both non-Lipschitz perturbation and impulse effects is studied in this paper. Based on the average dwell-time approach, a criterion is proposed which ensures that the system’s state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if we impose a bound on the initial condition. It is shown that the finite-time stability degree could be greater than one, which is quite different from the existing results for asymptotic stability. Moreover, the total activation time of the Schur stable subsystems does not need to be greater than that of the unstable subsystems. A numerical example is presented to illustrate the effectiveness of the proposed design method.

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbationFault tolerant control for singular systems with actuator saturation and nonlinear perturbation.

Abstract: In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems

Abstract: This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi–Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.

Robust finite-time stability and stabilisation of switched positive systems

Abstract: This study is concerned with robust finite-time stability and stabilisation of a class of switched positive systems. By using the multiple linear copositive Lyapunov function approach, sufficient conditions of finite-time stability and finite-time boundedness are constructed, respectively. l 1-gain is used to analyse the disturbance attenuation performance of the systems, and a finite-time weighted l 1-gain is obtained under bounded exogenous disturbances. Then, the problem of robust finite-time stabilisation of non-autonomous systems with a weighted l 1-gain is solved. All the proposed conditions are formulated in linear programming. Finally, two illustrative examples are given to show the validity of the theoretical results.

On Finite-Time Stability of Cyclic Switched Nonlinear Systems

Abstract: This technical note considers the global finite-time stability problem for a class of switched nonlinear systems with the cyclic switching sequence, dissipative or non-dissipative impulsive effects may appear at each switching instant, and each mode may or may not be finite-time stable individually. A new concept named cycle dwell time is proposed based on which two stability conditions are established. These conditions fully reveal the trade-off among each mode's dynamics, impulsive dynamics and initial conditions. An example of multi-agent systems illustrates the efficiency of the new results.

On finite-time stability for nonlinear impulsive switched systems

Abstract: This paper is concerned with the finite-time stability problem for switched systems subject to both nonlinear perturbation and impulse effects. The average dwell time approach, combined with the algebraic matrix theory, is utilized to derive a criterion guaranteeing that the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval. The requirement that at least one subsystem should be stable to ensure asymptotic stability is no longer necessary. Moreover, the finite-time stability degree could be positive, which is a relaxed condition for asymptotic stability. A numerical example is presented to illustrate the effectiveness of the proposed method.