On the observer design problem for continuous-time switched linear systems with unknown switchings

Gómez‐Gutiérrez, David; Čelikovský, Sergej; Ramírez-Treviño, A.; Castillo–Toledo, B.

doi:10.1016/j.jfranklin.2015.01.036

Cited by 45 publications

(30 citation statements)

References 42 publications

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“…An illustration of this argument, showing T max ( ) as a function of , with T c = 1s, is presented in Figure 2A. Although, by Theorem 2 the least upper bound of the settling time is T c = 1s, it can be seen that, in the best case, the bound (12) provides an overestimation of T c with = 1 K ( 1 (1−pk) + 1 (qk−1) )| p=0.5,q=3,k=1.5 = 1.1249. Moreover, in Figure 1A, it can be seen that, although the least upper bound of the settling-time function is T c = 1s, the upper bound estimation provided by (13) is T max ( )| =4 = 4.4331s.…”

Section: Settling Time Bound Analysis and Comparisonmentioning

confidence: 94%

“…Furthermore, in the case of switching systems, it is frequently required that the observer (or controller) achieves the stability of the observation error (or tracking error) before the next switching. 11,12 Lack of uniform boundedness of the settling-time function regardless of the initial conditions causes several restrictions to the practical application of finite time observer/controller. [13][14][15] These restrictions can be relaxed using the fixed-time stability concept.…”

Section: Introductionmentioning

confidence: 99%

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Enhancing the settling time estimation of a class of fixed‐time stable systems

Aldana‐López

Gómez‐Gutiérrez

Jiménez‐Rodríguez

et al. 2019

Intl J Robust & Nonlinear

188

155

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Summary In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.

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Section: Settling Time Bound Analysis and Comparisonmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Enhancing the settling time estimation of a class of fixed‐time stable systems

Aldana‐López

Gómez‐Gutiérrez

Jiménez‐Rodríguez

et al. 2019

Intl J Robust & Nonlinear

188

155

View full text Add to dashboard Cite

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“…In missile guidance, 21 the impact time control guidance laws require stabilization in a desired time 22,23 . In hybrid dynamical systems, it is frequently required that the observer (respectively, controller) stabilizes the observation error (respectively, tracking error) before the next switching occurs 24,25 . In the frequency control of an interconnected power network, not only is the frequency deviation of interest but also how long the frequency stays out of the bounds 26 .…”

Section: Introductionmentioning

confidence: 99%

On the design of nonautonomous fixed‐time controllers with a predefined upper bound of the settling time

Gómez‐Gutiérrez

2020

Intl J Robust & Nonlinear

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Recently, there has been a great deal of attention in a class of finite-time stable dynamical systems, called fixed-time stable, that exhibit uniform convergence with respect to its initial condition, that is, there exists an upper bound for the settling-time (UBST) function, independent of the initial condition of the system. Of particular interest is the development of stabilizing controllers where the desired UBST can be selected a priori by the user since it allows the design of controllers to satisfy real-time constraints. Unfortunately, existing methodologies for the design of controllers for fixed-time stability exhibit the following drawbacks: on the one hand, in methods based on autonomous systems, either the UBST is unknown or its estimate is very conservative, leading to over-engineered solutions; on the other hand, in methods based on time-varying gains, the gain tends to infinity, which makes these methods unrealizable in practice. To bridge these gaps, we introduce a design methodology to stabilize a perturbed chain of integrators in a fixed-time, with the desired UBST that can be set arbitrarily tight. Our approach consists of redesigning autonomous stabilizing controllers by adding time-varying gains. However, unlike existing methods, we provide sufficient conditions such that the time-varying gain remains bounded, making our approach realizable in practice. K E Y W O R D Sfixed-time control, predefined-time control, predefined-time stabilization, prescribed-time control INTRODUCTIONRecently, there has been a great deal of attention in the control community on the analysis of a class of systems, known as fixed-time stable systems, because they exhibit finite-time convergence with an upper bound of the settling time (UBST) that is independent of the initial conditions of the system. 1-5 This effort has produced many contributions on algorithms with the fixed-time convergence property, such as multiagent coordination, 6-9 distributed resource allocation, 10 synchronization of complex networks, 11,12 stabilizing controllers, 1,13-16 state observers, 17 and online differentiation algorithms. 18,19 The fixed-time stability property is of great interest in the development of algorithms for scenarios where real-time constraints need to be satisfied. In fault detection, isolation, and recovery schemes, 20 failing to recover from the fault on time may lead to an unrecoverable mode. In missile guidance, 21 the impact time control guidance laws require stabilization in a desired time. 22,23 In hybrid dynamical systems, it is frequently required that the observer (respectively, controller) Int J Robust Nonlinear Control. 2020;30:3871-3885.wileyonlinelibrary.com/journal/rnc

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“…This is usually referred to as the distinguishability problem. This problem, together with the SLS observability, has been extensively studied in the literature for the case of known in puts [1,9,13,18,20]. However, the observability of continuous-time SLS subject to unknown dis turbances and unknown switching signals has re ceived less attention.…”

mentioning

confidence: 99%

“…Based on the observability analysis here de rived, we show that if the perturbed SLS is ob servable, then for "almost every" input only one observer in the collection will converge to a zero output estimation error (the one associated to the evolving LS), thus inferring the evolving LS and obtaining the associated continuous state. Com pared to [1][2][3]6,9,12,12,13,20,22], the proposed approach addresses a wider class of SLS as un known disturbances are considered. Moreover, un like the recent results [19,22] where the switching signal is known, in our approach the continuous state together with the switching signal are inferred from the continuous output.…”

mentioning

confidence: 99%