Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Laila, Dina Shona; Astolfi, Alessandro

doi:10.1016/j.automatica.2005.06.003

Cited by 48 publications

(36 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…and for any a ∈ R + , there exists a K + -class functionγ satisfying (9). Then, HDS (1) has the first ISS property.…”

Section: Thain213mentioning

confidence: 99%

“…ISS has been successfully employed in the stability analysis and control synthesis of nonlinear systems. These works mainly focused on the following topics related to the study of the ISS property: feedback ISS stabilization for nonlinear systems [2,4,[9][10]13], ISS nonlinear small gain results for nonlinear systems [6,17,18], ISS for sampleddata systems [8], ISS problem using averaging technique [7], ISS properties of networked control systems [5], ISS for discrete-time systems [3], ISS for impulsive systems in [11][12]37], and ISS for time-delay systems in [14][15][16]39].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Input-to-state stability for a class of hybrid dynamical systems via hybrid time approach

Hill

Teo

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

View full text Add to dashboard Cite

Abstract-This paper studies the ISS (input-to-state stability) for a class of HDS (hybrid dynamical systems). By using the concept of hybrid time for HDS, two kinds of ISS notions are proposed. They are called the first ISS property and the second ISS property of HDS. By employing the ISS properties on continuous and/or discrete dynamics in the HDS, the first and second ISS properties for the whole HDS are investigated. We show that there exists the first ISS property for the whole HDS if any one of dynamics in the HDS has the ISS property and the dwell time on this dynamics is sufficiently long even if there is no ISS property for the other dynamics. Moreover, the second ISS property of HDS is derived for the cases in which one kind of dynamics without external inputs has a stability property while the other one has no stability and ISS properties. Finally, one example is given for illustration.

show abstract

“…and for any a ∈ R + , there exists a K + -class functionγ satisfying (9). Then, HDS (1) has the first ISS property.…”

Section: Thain213mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Input-to-state stability for a class of hybrid dynamical systems via hybrid time approach

Hill

Teo

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

View full text Add to dashboard Cite

show abstract

“…The notions of UIOS and UISS were formulated in [39,40,41,44,45] for finite-dimensional systems described by ordinary differential equations. More recently, sufficient conditions for semiglobal practical UISS were studied in [24,25] for sampled-data systems. In the present work, the sufficient conditions will be expressed in terms of a scalar and in terms of a vector Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

“…Teel and others, see [10,11,20,24,25,[31][32][33][34][35][36][37]49]). The results obtained in this way lead to a systematic procedure for the construction of practical, semi-global feedback stabilizers and provide a list of possible reasons that explain the occasional failure of sampled-data control mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Global stability results for systems under sampled‐data control

Karafyllis

Kravaris

2008

Intl J Robust & Nonlinear

102

View full text Add to dashboard Cite

show abstract

“…A range of tools has been developed to aid the controller design within this framework: construction of appropriate strict Lyapunov functions via change of supply rates techniques [15,26,27], stability of cascaded systems [23,24] and Matrosov theorem [22]. These results were used, for instance, to construct controllers based on approximate models using backstepping [25], optimization based stabilization [7], model predictive control [5], nonholonomic systems [13] and port controlled Hamiltonian systems [14]. Simulation comparisons in these references invariably show that controllers designed within our framework perform better than appropriate emulated controllers, see e.g.…”

mentioning

confidence: 99%

On Stability of Sets for Sampled-Data Nonlinear Inclusions via Their Approximate Discrete-Time Models and Summability Criteria

Nešić¹,

Lorı́a²,

Panteley³

et al. 2009

SIAM J. Control Optim.

View full text Add to dashboard Cite

On stability of sets for sampled-data nonlinear inclusions via their approximate discrete-time models and summability criteria. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2009Mathematics, , 48 (3), pp.1888Mathematics, -1913 Abstract. This paper consists of two main parts. In the first part, we provide a framework for stabilization of arbitrary (not necessarily compact) closed sets for sampled-data nonlinear differential inclusions via their approximate discrete-time models. We generalize [19, Theorem 1] in several different directions: we consider stabilization of arbitrary closed sets, plants described as sampleddata differential inclusions and arbitrary dynamic controllers in the form of difference inclusions. Our result does not require the knowledge of a Lyapunov function for the approximate model, which is a standing assumption in [21] and [19, Theorem 2]. We present checkable conditions that one can use to conclude semi-global asymptotic (SPA) stability, or global exponential stability (GES), of the sampled-data system via appropriate properties of its approximate discrete-time model.In the second part, we present sufficient conditions for stability of parameterized difference inclusions that involve various summability criteria on trajectories of the system to conclude global asymptotic stability (GAS), or GES, and they represent discrete-time counterparts of results given in [32]. These summability criteria are not Lyapunov based and they are tailored to be used within our above mentioned framework for stabilization of sampled-data differential inclusions via their approximate discrete-time models. We believe that these tools will be a useful addition to the toolbox for controller design for sampled-data nonlinear systems via their approximate discrete-time models.Key words. Sampled-data systems, stability, difference inclusions AMS subject classifications.1. Introduction. Although most controllers are nowadays implemented digitally using sample and hold devices, sampled data nonlinear control has received much less attention than continuous time nonlinear control. The controller design problem for sampled-data systems can be carried out in three essentially different ways: (i) emulation (design continuous time controller and then discretize the controller); (ii) discrete-time design (discretize the plant and design a discrete-time controller directly on the discrete time model); (iii) sampled-data design (use the real model of the sampled-data system that includes the inter-sample behavior to design the controller). For nonlinear systems, some results on emulation can be found in [16], while we are not aware of any results on sampled data design for nonlinear systems (details on the sampled data method for linear systems can be found in [4] and references cited therein).

show abstract

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Cited by 48 publications

References 27 publications

Input-to-state stability for a class of hybrid dynamical systems via hybrid time approach

Input-to-state stability for a class of hybrid dynamical systems via hybrid time approach

Global stability results for systems under sampled‐data control

On Stability of Sets for Sampled-Data Nonlinear Inclusions via Their Approximate Discrete-Time Models and Summability Criteria

Contact Info

Product

Resources

About