Stabilization of switched affine systems: An application to the buck-boost converter

Corona, Daniele; Buisson, Jean; Schutter, Bart De; Giua, Alessandro

doi:10.1109/acc.2007.4282539

Cited by 52 publications

(35 citation statements)

References 19 publications

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“…In this section, it will be presented two different switching functions for the H ∞ control design of the switched affine system (1)- (2). Both are based on a quadratic Lyapunov function v(ξ ) = ξ Pξ (11) with P > 0.…”

Section: State Feedback Control Designmentioning

confidence: 99%

“…Theorem 4: Consider system (1)- (2) and let x e ∈ R n x be given. If there exist λ ∈ , a positive definite matrix S ∈ R n x ×n x , symmetric matrices R i ∈ R n x ×n x , Z i ∈ R n w ×n w , matrices Y i ∈ R n u ×n x , J i ∈ R n x ×n w and a scalar ρ > 0 satisfying (15), and the conditions ⎡…”

Section: State-input Dependent Switching Functionmentioning

confidence: 99%

“…Switched systems have attracted the attention of the scientific community in the last decades because of their high potential for practical applications, as for instance, in power electronics [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

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State feedback ℋ _∞ control design of continuous‐time switched affine systems

Deaecto

Santos

2015

IET Control Theory & Applications

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This study deals with state feedback H ∞ control design of continuous-time switched affine systems. The main purpose is to design a set of state feedback gains together with a switching function assuring global asymptotic stability of a desired equilibrium point. The equilibrium point belongs to a set of attainable ones to be determined. Moreover, the control design must take into account a pre-specified upper bound to the L 2 gain from the external input to the controlled output. Two different switching functions are proposed and discussed. The first one depends only on the state and the other depends also on the external input. The results are compared with recent ones available in the literature to date, as for instance, those based on a max-type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons. IntroductionSwitched systems have attracted the attention of the scientific community in the last decades because of their high potential for practical applications, as for instance, in power electronics [1-3].They represent a subclass of hybrid systems characterised by having a switching rule that selects at each instant of time one of the available subsystems. This switching rule can be arbitrary, see [4], or a control variable that must be designed in order to assure stability and good performance for the overall system. Another possible control technique is based on sliding mode control, as it has been proposed in [5]. For switched linear systems, the literature presents several important results concerning the control design of a switching rule based on state feedback [6, 7] and on output feedback [8,9]. One interesting characteristic is that the switching strategy can assure global asymptotic stability even if all subsystems are unstable. Moreover, the recent paper [10] shows that, even if all subsystems are stable, a consistent switching rule can enhance the global performance when compared with that of each isolated subsystem. The articles [11][12][13] and the books [14,15] are surveys on this topic. Switched affine systems are more involved since they present several equilibrium points composing a region on the state space. Hence, the control goals consist in determining a set of attainable equilibrium points and a switching rule that guides any trajectory of the system, starting from an arbitrary initial condition, to the desired equilibrium, which can not be shared by any of the subsystems. The literature presents some results about stabilisation based on optimal control, see [2,16,17], and on Lyapunov method approach, see [1,3,[18][19][20][21][22][23][24][25], where [19,25] deal with sampled-data implementation. Most of them, as for instance, [3,18] are based on a quadratic Lyapunov function and show that the existence of a stable convex combination of the subsystems state-space matrices is a sufficient condition for global asymptotic stability. Another recent technique is based on a max-type Lyapunov ...

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Section: State Feedback Control Designmentioning

confidence: 99%

Section: State-input Dependent Switching Functionmentioning

confidence: 99%

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State feedback ℋ _∞ control design of continuous‐time switched affine systems

Deaecto

Santos

2015

IET Control Theory & Applications

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“…L is the inductance, C is the capacitance, and R denotes the load resistance. In recent years, the class of power converters is modeled as switched system and the corresponding stabilization problem has also been investigated in [28,29]. As done in [28,29], by introducing variables = t∕T, L 1 = L∕T and C 1 = C∕T, The circuit system is characterized by…”

Section: Illustrative Examplesmentioning

confidence: 99%

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Zheng

Sun

Ren

et al. 2017

Asian Journal of Control

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This paper is concerned with the stability and stabilization problem of a class of discrete-time switched systems with mode-dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode-dependent (MD) and quasi-time-dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD H ∞ controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H ∞ performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results.Definition 2. For a switching signal (t) and any T ≥ t ≥ 0, let N p (T, t) be the switching numbers and the p th subsystem is activated over the interval [t, T]. T p (T, t) denotes the total running time of the p th subsystem over the interval [t, T] with p ∈ . We say that (t) has a mode-dependent average dwell time p if there exists a positive number N 0p (We call N 0p the mode-dependent chatter bounds here) and p satisfyDefinition 3 ([26]). For > 0, system (1)-(2) is said to be GUAS with an l 2 -gain, if under zero initial condition, system (1)-(2) is GUAS and ‖z‖ l 2 [0,T] ≤ ‖ ‖ l 2 [0,T] holds for all nonzero ∈ l 2 [0, T], 0 ≤ T < ∞.Definition 4. For > 0 and let 0 < < 1, the switched system (1)-(2) is said to be GUAS with an l 2 -gain, if under zero initial condition, system (1)-(2) is GUAS and ∑ ∞ k=k 0(1 − )z T (k)z(k) ≤ ∑ ∞ k=k 0

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“…According to the same normalization technique used in [26], the closed-loop systems matrices can be given by…”

Section: Examplementioning

confidence: 99%

Fault Detection for a Class of Impulsive Switched Systems

Dai

et al. 2014

Int. J. Autom. Comput.

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Abstract:The problem of fault detection for a class of nonlinear impulsive switched systems is investigated in this paper. Fault detection filters are designed such that the augmented systems are stable, and the residual error signal generated by the filters guarantees the H∞ performance for disturbances and faults. Sufficient conditions for the design of fault detection (FD) filters are presented by linear matrix inequalities. Moreover, the filter gains are characterized according to a solution of a convex optimization. Finally, an example derived from a pulse-width-modulation-driven boost converter is given to illustrate the effectiveness of the FD design approach.

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Stabilization of switched affine systems: An application to the buck-boost converter

Cited by 52 publications

References 19 publications

State feedback ℋ _∞ control design of continuous‐time switched affine systems

State feedback ℋ _∞ control design of continuous‐time switched affine systems

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Fault Detection for a Class of Impulsive Switched Systems

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Stabilization of switched affine systems: An application to the buck-boost converter

Cited by 52 publications

References 19 publications

State feedback ℋ ∞ control design of continuous‐time switched affine systems

State feedback ℋ ∞ control design of continuous‐time switched affine systems

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

Fault Detection for a Class of Impulsive Switched Systems

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State feedback ℋ _∞ control design of continuous‐time switched affine systems

State feedback ℋ _∞ control design of continuous‐time switched affine systems