Robust estimation of linear switched systems with dwell time

Allerhand, Liron I.; Shaked, U.

doi:10.1080/00207179.2013.822104

Cited by 9 publications

(9 citation statements)

References 17 publications

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“…Since then, clock-dependent conditions have been used for the analysis and control of switched, impulsive, sampleddata and LPV systems; see e.g. [47,[60][61][62][63][64][65][66][67][68]. Such results have also been applied to more practical problems such as fault tolerant control [69,70] or estimation [62,71].…”

Section: Introductionmentioning

confidence: 99%

“…The first one relies on a discretization approach which is largely inspired from [60] and where the infinite-dimensional decision variable is assumed to be continuous and piecewise linear. This method has also been considered, in turn, in [59,61,62,64,67,73]. By doing so, the infinite-dimensional program becomes finite-dimensional and can be solved using conventional algorithms such as interior point methods; see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Briat

2017

Nonlinear Analysis: Hybrid Systems

147

126

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Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finite-dimensional or semi-infinite linear programs. To be applicable to uncertain systems and to control design, a lifting approach introducing a clock-variable is then considered in order to make the conditions affine in the matrices of the system. The resulting stability and stabilization conditions are stated as infinitedimensional linear programs for which three asymptotically exact computational methods are proposed and compared with each other on numerical examples. Similar results are then obtained for linear positive switched systems by exploiting the possibility of reformulating a switched system as an impulsive system. Some existing stability conditions are retrieved and extended to stabilization using the proposed lifting approach. Several examples are finally given for illustration.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Briat

2017

Nonlinear Analysis: Hybrid Systems

147

126

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“…Allerhand and Shaked 9,10 obtained state-feedback synthesis conditions for uncertain switched linear systems subject to dwell-time constraints that permit the design of a switched state-feedback control law that meets a closed-loop L2-performance objective. Similarly, piecewise linear quadratic Lyapunov functions are used in Allerhand and Shaked 11 for the design of robust state estimation filters.…”

Section: Introductionmentioning

confidence: 99%

Switched H₂-state-feedback control with application to a fighter aircraft

Kemer

Başak

Prempain

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

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This paper proposes two different [Formula: see text]-state-feedback controller synthesis algorithms for uncertain linear, time-varying, switched systems. The synthesis algorithms are based on a dwell-time approach, which makes use of time-varying parameter-dependent Lyapunov functions. The control laws consist of state-feedback controllers that are switched according to external signals. The proposed synthesis algorithms are then employed to design switched [Formula: see text]-state-feedback control laws for the longitudinal dynamics of the ADMIRE fighter benchmark model. The results obtained in simulation show the merits of the proposed approach.

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“…The motivation for the study of such systems stems from two aspects. On the one hand, so many real‐world systems can be modelled as switched systems, such as chemical systems, power systems and communication networks [9–14]. On the other hand, the switching control strategy has been widely used in various advanced controls, such as in [15–20].…”

Section: Introductionmentioning

confidence: 99%

State‐constrained robust stabilisation for a class of high‐order switched non‐linear systems

Niu

Xiang

2015

IET Control Theory & Applications

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This study deals with the problem of robust stabilisation for a class of state-constrained high-order uncertain switched non-linear systems in lower triangular form. Bounded state-feedback controllers are designed to assure that asymptotic stabilisation is achieved in a domain without violation of the state constraint, and all closed-loop signals are bounded, when an appropriate requirement on the initial condition is imposed. Simulation results are provided to show the efficiency of the developed method. IntroductionDuring the past few decades, switched systems have received considerable attention [1][2][3][4][5][6][7][8]. The motivation for the study of such systems stems from two aspects. On the one hand, so many realworld systems can be modelled as switched systems, such as chemical systems, power systems and communication networks [9][10][11][12][13][14]. On the other hand, the switching control strategy has been widely used in various advanced controls, such as in [15][16][17][18][19][20]. When the switching law has no given mode (or is arbitrary), one way to investigate the stability and stabilisation problems is to find a common Lyapunov function (CLF) for all the subsystems. However, finding a CLF for a family of subsystems is still an open problem, even though some progress has been made [21][22][23][24]. Backstepping design technique is a power tool for constructing stabilising controller for non-linear systems in lower triangular form, and many significant developments have been achieved based on this technique [25][26][27][28][29][30]. This design method is, of course, expected to be useful for stabilising a switched non-linear system. However, according to the standard backstepping procedure, backstepping cannot be directly extended to the switched non-linear system in lower triangular form because of the different coordinate transformations for different subsystems [31,32]. Furthermore, the so-called adding a power integrator backstepping design method is proposed in [33][34][35][36], which is used in the controller design for high-order non-linear systems. Nevertheless, there exist only a few results on high-order switched non-linear system in lower triangular form [37,38]. In addition, it is worth pointing out that many systems in practice have states/output constraints. Therefore the constrained control problem of switched systems is of great significance. Unfortunately, these constraints are not widespreadly taken into account in the aforementioned papers. A few exceptions are [39], in which tracking control for switched lower triangular systems with time-varying output constraints is achieved, and [40], which proposed a control design method for a class of switched non-linear systems with full state constraints.On the other hand, there exist several techniques to solve the constrained control problem for linear systems and non-linear systems. In the literature, most of the results are based on the notions of set invariance and admissible set control [41,42]. Model predictive control that repre...

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Robust estimation of linear switched systems with dwell time

Cited by 9 publications

References 17 publications

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Switched H₂-state-feedback control with application to a fighter aircraft

State‐constrained robust stabilisation for a class of high‐order switched non‐linear systems

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Robust estimation of linear switched systems with dwell time

Cited by 9 publications

References 17 publications

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Switched H2-state-feedback control with application to a fighter aircraft

State‐constrained robust stabilisation for a class of high‐order switched non‐linear systems

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Switched H₂-state-feedback control with application to a fighter aircraft