On invariant polyhedra of continuous-time systems subject to additive disturbances

Milani, B.E.A.; Dórea, Carlos Eduardo Trabuco

doi:10.1016/0005-1098(96)00002-7

Cited by 22 publications

(9 citation statements)

References 7 publications

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“…In the light of Theorems 2, 3 and 4, we get a method of verifying the criterion (8). For each k 0 ∈ {1, 2, · · · , t}, set (16), then determine its consistency, i.e., determining the consistency of following system of linear inequalities:…”

Section: Theorem 3 Let a And B Be As Inmentioning

confidence: 99%

“…The other one is to design a viable solution within a viable set. Viability conditions for a linear control system has been studied extensively in recent years, see [6][7][8]. Although a necessary and sufficient viability condition for a differential inclusion was given in [9][10][11], it is a hard work to check that condition in most applications directly.…”

Section: Introductionmentioning

confidence: 99%

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Viability criteria for differential inclusions

Gao

2011

J Syst Sci Complex

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A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.

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Section: Theorem 3 Let a And B Be As Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Viability criteria for differential inclusions

Gao

2011

J Syst Sci Complex

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“…As shown by Milani and Dórea (1996), the existence of admissible matrices W 2 and W 3 satisfying relations (24)-(25) is related to the following null-space intersections:…”

Section: General Commentsmentioning

confidence: 99%

“…The use of the positive invariance property in the control of constrained dynamical systems has been receiving much attention in the last years (Blanchini, 1990;Blanchini, 1994;De Santis, 1994;Georgiou and Krikelis, 1991;Gilbert and Tan, 1991;Hennet, 1989;Hennet and Béziat, 1991;Kolmanovski and Gilbert, 1995;Milani and Dórea, 1996;Tarbouriech and Gomes da Silva Jr., 1997;Tarbouriech and Castelan, 1993;Tarbouriech and Castelan, 1995). This property is used, for instance, to guarantee the maintenance of the state trajectories of a controlled system in the interior of some prescribed sets of admissible states determined from some sets of control or state constraints.…”

Section: Introductionmentioning

confidence: 99%

Simple and weak delta-invariant psolyhedral sets for discrete-time singular systems

Castelan

Tarbouriech²

2003

Sba Controle & Automação

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In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of delta-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak delta-invariance are considered. They can be seen as extensions of the delta-positive invariance concept used for the regular linear systems with additive disturbances. The results are presented by considering classical equivalent system representations for linear singular systems.
Apresentam-se condições necessárias e suficientes para a invariância positiva de poliédros convexos relativamente a um sistema singular, linear e em tempo discreto, sujeito a perturbações aditivas e limitadas. Introduz-se as noções de delta-invariância simples e de delta-invariância fraca, associadas a diferentes hipóteses a serem verificadas pelas condições iniciais. Estas noções podem ser consideradas como extensões, para o caso de sistemas singulares, do conceito de delta-invariância utilizado no caso de sistemas regulares sujeitos a perturbações. Os resultados são desenvolvidos a partir de duas formas usuais de representação de sistemas singulares lineares

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“…Another one is to design a viable solution within a viable set. Viability conditions for a linear control system have been studied widely in recent years; see [15,16]. A necessary and sufficient viability condition for a differential inclusion was given in [8,17], but it is a hard work to check that condition in most applications directly.…”

Section: Introductionmentioning

confidence: 99%

Viability Discrimination of a Class of Control Systems on a Nonsmooth Region

Zhao

Yang

et al. 2014

Discrete Dynamics in Nature and Society

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The viability problem is an important field of study in control theory; the corresponding research has profound significance in both theory and practice. In this paper, we consider the viability for both an affine nonlinear hybrid system and a hybrid differential inclusion on a region with subdifferentiable boundary. Based on the nonsmooth analysis theory, we obtain a method to verify the viability condition at a point, when the boundary function of the region is subdifferentiable and its subdifferential is convex hull of many finite points.

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On invariant polyhedra of continuous-time systems subject to additive disturbances

Cited by 22 publications

References 7 publications

Viability criteria for differential inclusions

Viability criteria for differential inclusions

Simple and weak delta-invariant psolyhedral sets for discrete-time singular systems

Viability Discrimination of a Class of Control Systems on a Nonsmooth Region

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