Interval criterion for stability analysis of discrete-time nural networks with partial state saturation nonlinearities

Kolev, Lubomir V.; Petrakieva, Simona; Mladenov, Valeri

doi:10.1109/neurel.2004.1416520

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…Proof From Lemma 2, we know for any initial state x(0) ∈ (℘(n, n p1 ) ∩ ε(P, 1)) that the state of system (6) can be attracted to zero. Obviously, (℘(n, n p1 ) ∩ ε(P, 1)) ⊂ ℘(n, n p1 ).…”

Section: A Condition For Set Invariancementioning

confidence: 99%

“…By the property of Lemma 1, in ℘(n, n p1 ), the constructed system (6) is with the same domain of attraction as the original system (3), the proof is similar to that of Lemma 1, and it is omitted here. Therefore, in the following, we can study system (3) with the aid of system (6).…”

Section: A Condition For Set Invariancementioning

confidence: 99%

“…Control systems with state saturation are often encountered in a variety of applications, including signal processing, recurrent neural networks, and control systems, and have been studied extensively (see, e.g., [1][2][3][4][5][6][7], and the references therein). When there is state saturation in control systems, most of such systems can be modeled by statespace representations with polyhedral or ellipsoidal state constraints, and the global stability of an otherwise stable linear closed-loop system cannot be ensured in general.…”

Section: Introductionmentioning

confidence: 99%

“…For higher-order systems, various sufficient conditions for the global asymptotic stability were identified (see, e.g., [6,10], and the references therein). Under the sufficient condition of [11], any system trajectory starting from inside the state saturation region will never reach the boundary of it, i.e., the state never saturates.…”

Section: Introductionmentioning

confidence: 99%

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A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

Guan

Yang

2011

J. Control Theory Appl.

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The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as 'large' as possible. An example is provided to demonstrate the effectiveness of the new method.

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Section: A Condition For Set Invariancementioning

confidence: 99%

Section: A Condition For Set Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

Guan

Yang

2011

J. Control Theory Appl.

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“…erefore, it is significant to explore the filter issue of positive systems with state saturation. Derong Liu and Michel [17] analyzed the stability of systems with partial state saturation nonlinearities using the Lyapunov function approach, and Kolev et al [18] addressed the state saturation nonlinearities for discrete-time neural networks. Ji et al [19] were concerned with the stability analysis of discrete-time linear systems with state saturation using a saturation-dependent Lyapunov functional.…”

Section: Introductionmentioning

confidence: 99%

Event-Triggered Asynchronous Filter of Positive Switched Systems with State Saturation

Lin

Zhang

2022

Mathematical Problems in Engineering

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This paper investigates the event-triggered asynchronous filter of positive switched systems with state saturation using linear programming and multiple Lyapunov functions. First, a filter is constructed for continuous-time positive switched systems. Under the asynchronous switching law, an error system is proposed with respect to positive switched systems and their filters, where the state saturation term is described in a polytopic form by virtue of the saturation property. A novel event-triggering condition is addressed based on a 1-norm inequality. Under the event-triggering condition, the error system is transformed into an interval system with lower and upper bounds. By using multiple Lyapunov functions and linear programming, the positivity and stability of the error system are achieved by considering the corresponding properties of the lower and upper bounds, respectively. Then, the event-triggered l1-gain filter and nonfragile filter are also proposed for the systems with disturbances. Moreover, the presented filter framework is extended to the discrete-time case. Finally, two examples are given to verify the effectiveness of the proposed filters.

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Analysis and design of output feedback control systems in the presence of actuator saturation

Guan

Yang

2009

2009 American Control Conference

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In this paper, a dynamic output feedback controller design approach based on cone complementary linearisation procedure is proposed for linear time-invariant (LTI) systems with actuator saturation. Firstly, the estimation of domain of attraction is given. Then, a design method to find a larger estimation of domain of attraction is presented. In the process of design, nonconvex conditions are obtained, so a cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. Two examples are given to illustrate the efficiency of the design method.

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Interval criterion for stability analysis of discrete-time nural networks with partial state saturation nonlinearities

Cited by 5 publications

References 7 publications

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

Event-Triggered Asynchronous Filter of Positive Switched Systems with State Saturation

Analysis and design of output feedback control systems in the presence of actuator saturation

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