Input–output finite-time stabilisation of a class of hybrid systems via static output feedback

Amato, Francesco; Carannante, G.; Tommasi, G. De

doi:10.1080/00207179.2011.589082

Cited by 36 publications

(13 citation statements)

References 18 publications

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“…Some related results have been obtained in [18][19][20][21][22][23][24][25]. These results about IO-FTS are mainly involved in impulsive systems [18], linear systems [19][20][21][22], stochastic systems [23], Markovian jump systems [24], and impulsive switched linear systems [25]. It is worth noting that the results mentioned above are mainly concerned with nonpositive systems.…”

Section: Introductionmentioning

confidence: 95%

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

Liu¹,

Cao²,

Fu³

et al. 2017

Journal of Control Science and Engineering

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The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 95%

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

Liu¹,

Cao²,

Fu³

et al. 2017

Journal of Control Science and Engineering

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“…Therefore, some analysis methods of time-varying systems have been extended to impulsive systems in recent years. For examples, differential matrix inequality (DMI)-based conditions for finite-time stability of linear impulsive deterministic systems (LIDSs) were obtained in the works of Amato et al, 22,23 and by using a quadratic time-varying Lyapunov function approach 24,25 or looped Lyapunov function, 25,26 dwell-time-based stability criteria for LIDSs were established in terms of DMIs. Since the time-varying Lyapunov function can capture the hybrid characteristics of LIDSs, these results are adapted to CUDU-type Notation 1.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and synthesis for linear impulsive stochastic systems

Luo

Deng

Chen

2018

Intl J Robust & Nonlinear

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SummaryThis paper presents a general framework for analyzing stability of linear impulsive stochastic systems (LISSs). Some simple mean square stability criteria for the three types of LISSs are firstly derived by analyzing an equivalent system. By exploring the hybrid characteristics of impulsive systems, the novel quasi‐periodic composite polynomial Lyapunov function and the time‐varying discretized Lyapunov function are developed, which leads to unified dwell‐time–based criteria for mean square stability and almost sure stability of LISSs without imposing the stability condition on continuous‐ and discrete‐time dynamics. Next, based on the established stability criteria, the synthesis problem of state‐feedback controller is solved. The computational complexity and the comparison with existing results on the deterministic systems are discussed. Finally, numerical examples are provided to illustrate the usefulness of the proposed results.

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“…IO-FTS involves signals defined over a finite-time interval and does not necessarily require the inputs and outputs to belong to the same class, and IO-FTS constraints permit specifying quantitative bounds on the controlled variables to be fulfilled during the transient response [6,7]. Some related results are also presented, such as linear systems [8], hybrid systems via static output feedback [9], nonlinear systems via sliding mode control [10], discrete-time impulsive switch systems [11], nonlinear stochastic systems [12], and Markovian jump systems [13,14].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Observer‐Based Input‐Output Finite‐Time Control of a Class of Nonlinear Systems

Liu¹,

Song²,

Fu³

et al. 2017

Mathematical Problems in Engineering

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This paper is concerned with disturbance observer-based input-output finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as multiple disturbances. Firstly, a disturbance observer is constructed to estimate the disturbance generated by an exogenous system. Secondly, by integrating the estimation of disturbance with a classical state feedback control law, a composite control law is designed and sufficient conditions for input-output finite-time stability (IO-FTS) of the closed-loop system are attained. Such conditions can be converted into linear matrix inequalities (LMIs). Finally, two examples are given to show the effectiveness of the proposed method.

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Input–output finite-time stabilisation of a class of hybrid systems via static output feedback

Cited by 36 publications

References 18 publications

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

Stability analysis and synthesis for linear impulsive stochastic systems

Disturbance Observer‐Based Input‐Output Finite‐Time Control of a Class of Nonlinear Systems

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