Detectability and Uniform Global Asymptotic Stability in Switched Nonlinear Time-Varying Systems

Lee, Ti-Chung; Tan, Ying; Mareels, Iven

doi:10.1109/tac.2019.2919672

Cited by 9 publications

(12 citation statements)

References 41 publications

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“…It is worthwhile to highlight that some early attempts 1 A weak Lyapunov function is a positive definite function whose derivative along the trajectories of dynamics is negative semi-definite. arXiv:2006.02021v1 [eess.SY] 3 Jun 2020 2 [25], [26], [33] on a switched NLTV system followed this direction with the assumption that the switched NTLV system has a weak Lyapunov function, and gave the generalization of the so-called Krasovskii-LaSalle theorem, which requires stronger assumptions than that in the classical LaSalle invariance principle. For switched NLTV systems, such results can only guarantee the convergence of an equilibrium point (or a compact set).…”

Section: Introductionmentioning

confidence: 99%

“…This paper focuses on direct extensions of the classic LaSalle invariance principle and the integral invariance principle to switched NLTV systems allowing for a general class of switching signals without any dwell-time constraints. Particularly, by utilizing the concept of virtual output and the corresponding observability condition as in [1], [3], [21], [35], the needed extensions naturally links to the recently developed framework in [26]. This framework employs the concept of limiting zeroing output solutions, resulting in techniques such as changing state functions (dynamics) and output functions (output signals).…”

Section: Introductionmentioning

confidence: 99%

“…This framework employs the concept of limiting zeroing output solutions, resulting in techniques such as changing state functions (dynamics) and output functions (output signals). These techniques provide great flexibility in checking the appropriate observability (see examples presented in [26]).…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, this paper explores the concept of the virtual output to check uniform global attractivity (UGA) with respect to initial time instants and a large class of switching signals when the switched NLTV system is already UGUB. In the sequel, the techniques of changing dynamics and output signals presented in [26] are modified accordingly. Moreover, the integral invariance principle can be extended to switched NLTV systems as well.…”

Section: Introductionmentioning

confidence: 99%

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Invariance Principles and Observability in Switched Systems With an Application in Consensus

Lee

Tan

et al. 2021

IEEE Trans. Automat. Contr.

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Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak observability (WO) associated with this output. WO is what the output informs about the limiting behavior of state trajectories (hidden in the zero locus of the output). In the context of switched NLTV systems, WO can be explored using the recently established framework of limiting zeroing-output solutions. Adding to this, an extension of the integral invariance principle for switched NLTV systems with a new method to guarantee uniform global attractivity of a closed set (without assuming uniform Lyapunov stability or dwell-time conditions) is proposed. By way of illustrating the proposed method, a leaderless consensus problem for nonholonomic mobile robots with a switching communication topology is addressed, yielding a new control strategy and a new convergence result.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Invariance Principles and Observability in Switched Systems With an Application in Consensus

Lee

Tan

et al. 2021

IEEE Trans. Automat. Contr.

Self Cite

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“…Generally, these tools make Lyapunov stability very complex (see [24,25]). Because, still there is an idea in the literature, constructing Lyapunov functions for nonlinear systems is a difficult task [26,27]. But, for the first and second order ordinary differential equations we highly simplified Lyapunov stability theory with LRC circuit systems.…”

Section: Introductionmentioning

confidence: 99%

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Ateş¹,

Kadah²

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.

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Circuit theory approach to stability and passivity analysis of nonlinear dynamical systems

Ateş

2021

Circuit Theory & Apps

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In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear time-varying systems controlled by a secondorder vector differential equation. First, we obtain this equation from a nonlinear time varying network of the circuit theory. Then, we construct the Lyapunov candidate function directly from the physical meaning of the given system. By the way, we review a number of previous results from the point view of Lyapunov's direct method. Our system with its real energy function generalize and improve upon some well-known studies. The new concept facilitates the formulation of the energy (Lyapunov) function from the powerenergy relationship of the given system. Then, we also realized that the time derivative of the Lyapunov function for a given dynamical systems is the negative value of the power dissipated in the system. Therefore, with the proposed approach, one can inspect the result of the time derivative of the energy function for a given physical system. Finally, two examples (one with simulations) are used to illustrate the superiority and validity of the obtained results.

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Detectability and Uniform Global Asymptotic Stability in Switched Nonlinear Time-Varying Systems

Cited by 9 publications

References 41 publications

Invariance Principles and Observability in Switched Systems With an Application in Consensus

Invariance Principles and Observability in Switched Systems With an Application in Consensus

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Circuit theory approach to stability and passivity analysis of nonlinear dynamical systems

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