A polynomial approach for stability analysis of switched systems

Mojica‐Nava, Eduardo; Quijano, Nicanor; Rakoto-Ravalontsalama, Naly; Gauthier, Alain

doi:10.1016/j.sysconle.2009.12.004

Cited by 57 publications

(29 citation statements)

References 14 publications

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“…Using this inductive argument above, we conclude that at Step n, there exist a common output-feedback controller of different subsystems and the update law as (38) where nk is defined by (28) with j = n. Remark 2: According to the design procedure, we can also design the different output-feedback controllers and the update law for different subsystems…”

Section: ) Inductivementioning

confidence: 99%

“…An important reason for the wide interest in the study of these problems is the variety of fields where the systems involved can be effectively modeled as switched systems. Such systems include robotic, mechatronic and mechanical systems, gene regulatory networks, switching power converters [19], [20], [28], just name a few. However, a switched system does not necessarily inherit properties of the individual subsystems [1], [27], [30], [41].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time

Long

Zhao

2015

IEEE Trans. Neural Netw. Learning Syst.

257

133

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This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed.

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Section: ) Inductivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time

Long

Zhao

2015

IEEE Trans. Neural Netw. Learning Syst.

257

133

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“…As we all know, for asymptotical stability of switched systems, it is a sufficient and necessary condition that there is a common Lyapunov function . However, finding a common Lyapunov function for switched systems is still an open problem, even though there has been some progress made on this issue for some kinds of switched systems with special structures …”

Section: Introductionmentioning

confidence: 99%

“…[22][23][24]27,28 However, finding a common Lyapunov function for switched systems is still an open problem, even though there has been some progress made on this issue for some kinds of switched systems with special structures. 30,31 In order to investigate the design of the output-feedback control laws for nonlinear systems in a constructive way, APIA is a powerful tool and was widely adopted. 14,15,17,18,[32][33][34] In the work of Lin et al, 15 by virtue of APIA, output-feedback stabilization for planar switched nonlinear systems has been addressed.…”

Section: Introductionmentioning

confidence: 99%

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

Lin

Park

2020

Intl J Robust & Nonlinear

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Summary In this paper, globally asymptotical stabilization problem for a class of planar switched nonlinear systems with an output constraint via smooth output feedback is investigated. To prevent output constraint violation, a common tangent‐type barrier Lyapunov function (tan‐BLF) is developed. Adding a power integrator approach (APIA) is revamped to systematically design state‐feedback stabilizing control laws incorporating the common tan‐BLF. Then, based on the designed state‐feedback controllers and a constructed common nonlinear observer, smooth output‐feedback controllers, which can make the system output meet the predefined constraint during operation, are proposed to deal with the globally asymptotical stabilization problem of planar switched nonlinear systems under arbitrary switchings. A numerical example is employed to verify the proposed method.

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“…Stateof-the-art methods for analyzing stability and stabilizability issues are provided in the survey paper [8] and in the more recent journal articles [9]- [11]. Novel techniques for control system synthesis are presented, e.g., in [12], [13] as to LQR optimal control, in [14], [15] as to H 2 and H ∞ control, in [16]- [19] as to output regulation, in [20], [21] as to model matching, in [22]- [26] as to inaccessible signal rejection, and in [27], [28] as to measurable signal rejection.…”

Section: Introductionmentioning

confidence: 99%

Measurable disturbance rejection with stability in continuous-time switched linear systems under dwell-time switching

Zattoni

2014

2014 European Control Conference (ECC)

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This work deals with rejection of disturbance inputs accessible for measurement in continuous-time switched linear systems with dwell-time constraints on the switching signals. The measurable disturbance rejection problem is stated as the problem of finding a dynamic feedforward switched compensator achieving zero output and exponential stability of the compensated switched linear system over a class of switching signals with a sufficiently large dwell-time, in the presence of any admissible measurable disturbance input. The synthesis of the compensator is based on a pair of sufficient conditions which respectively address the structural issue and the stabilizability issue. The former condition is expressed in geometric terms as the inclusion of the image of the disturbance input matrix in the sum of the so-called maximal robust controlled invariant subspace and the image of the control input matrix, for all the modes of the given switched system. The second condition is expressed as the exponential stabilizability under dwell-time switching of the internal switched dynamics of the maximal robust controlled invariant subspace.

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A polynomial approach for stability analysis of switched systems

Cited by 57 publications

References 14 publications

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time

Output‐feedback stabilization for planar output‐constrained switched nonlinear systems

Measurable disturbance rejection with stability in continuous-time switched linear systems under dwell-time switching

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