Lyapunov-Equation-Based Stability Analysis for Switched Linear Systems and Its Application to Switched Adaptive Control

In this paper, a novel hysteresis-based current control approach is presented. The basis of the developed control approach is the theory of switched systems, in particular, the system class of switched systems with multiple equilibria. The proposed approach guarantees the convergence of the state trajectory into a region around a reference trajectory by selective switching between the individual subsystems. Here, the reference trajectory is allowed to be time varying, but lies within the state space spanned by the subsystem equilibria. Since already published approaches only show convergence to a common equilibrium of all subsystems, the extension to the mentioned state space is a significant novelty. Moreover, the approach is not limited to the number of state variables, nor to the number of subsystems. Thus, the applicability to a large number of systems is given. In the course of the paper, the theoretical basics of the approach are first explained by referring to a trivial example system. Then, it is shown how the theory can be applied to a practical application of a voltage source converter that is connected to a permanent-magnet synchronous motor. After deriving the limits of the presented control strategy, a simulation study confirms the applicability on the converter system. The paper closes with a detailed discussion about the given results.

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“…With regard to the Lyapunov theory [20][21][22], it is suggested to specify the quality functions as…”

Section: Selection Of the Quality Functionsmentioning

confidence: 99%

“…holds. It can be noticed that both quotients in (20) are a measure for the convergence to the subsystem equlibria x eq,s . When V s (x eq,s (t)) is a candidate Lyapunov function and a constant reference point x ref (t) = const.…”

Section: Selection Of the Quality Functionsmentioning

confidence: 99%

Hysteresis-Based Current Control Approach by Means of the Theory of Switched Systems

Thielmann

Hans

2021

Applied Sciences

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“…Switching systems are classified into arbitrary and restricted categories according to the switching signal. Stability testing methods of these systems vary according to the type of switching system, but like other linear and nonlinear systems, they are usually based on the selection of the Lyapunov function [6,7]. Because of the switching property and creation of complex behavior in switchable systems, their stability assessment is essential to researchers, and thus, they have investigated various methods for switched systems including stability analysis [8], observability analysis [9,10], H∞ control [11][12][13], and optimal control [16,17].…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive control for a class of nonlinear switched systems using state-dependent switching

Noghredani

Pariz

2021

SN Appl. Sci.

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This paper presents a novel adaptive control for a class of nonlinear switched systems by introducing a sufficient condition for stabilization. Based on the possible instability of all sub-systems, a variable structure (VS) switching rule with an adaptive approach and sliding sector was offered. Moreover, the stability condition of the system can be determined by solving linear matrix inequalities (LMIs) to ensure asymptotic stability. The application of H∞ analysis of nonlinear switched systems was also investigated through the design of the mentioned adaptive control system and defining a VS switching rule. Finally, simulation results were presented to validate the novelty of the proposed method.

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“…In addition, as an iterative design method, backstepping technique has provided a structured and systematic method for Lyapunov function design of complex nonlinear systems 1‐3 . To go further, universal approximators such as neural network (NN) and fuzzy‐logic system have been introduced to handle unknown dynamics 4‐6 . Approximation‐based adaptive backstepping controller design has been widely applied in industrial control systems including robot control, 7 flight control, 8‐10 and so forth 11‐13 …”

Section: Introductionmentioning

confidence: 99%

Barrier Lypunov functions‐based nonsingular fixed‐time switching control for strict‐feedback nonlinear dynamics with full state constraints

Zhang

Dong

et al. 2021

Intl J Robust & Nonlinear

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This work proposes a nonsingular adaptive fixed‐time switching control method for a class of strict‐feedback nonlinear dynamics subject to full state constraints. The peculiarity of this design lies in overcoming the singularity issue that typically appears in the existing backstepping‐based fixed‐time control methods caused by the iterative differentiation of fractional power terms as tracking errors approach to zero, while guaranteeing the nonviolation of full state constraints. Crucial in solving such singularity issue is to skillfully introduce a smooth switching between fractional power and integer power terms, which guarantees that fractional power term is confined within a positive interval all the time. An asymmetric time‐varying barrier Lyapunov function is delicately incorporated into control design, rendering state variables to be within prescribed time‐varying bounds. Besides, radial basis function neural network is employed to handle system unknown nonlinearities. It is rigorously proved that all the closed‐loop signals eventually converge to small regions around origin within fixed‐time. Comparative simulation results are finally given to validate the effectiveness and superiority of the proposed control strategy.

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Lyapunov-Equation-Based Stability Analysis for Switched Linear Systems and Its Application to Switched Adaptive Control

Cited by 52 publications

References 24 publications

Hysteresis-Based Current Control Approach by Means of the Theory of Switched Systems

Hysteresis-Based Current Control Approach by Means of the Theory of Switched Systems

Robust adaptive control for a class of nonlinear switched systems using state-dependent switching

Barrier Lypunov functions‐based nonsingular fixed‐time switching control for strict‐feedback nonlinear dynamics with full state constraints

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