Complexity-driven construction of controlled invariant polytopic sets

In this article, the problem of constructing controlled invariant polytopic sets of a specified complexity, for discrete-time linear systems subject to linear state and control constraints, is investigated. First, geometric conditions for enlarging a polytopic set such that the resulting polytopic set has an a priori chosen number of vertices are formulated. Next, results concerning the enlargement of controlled invariant sets such that the resulting set remains controlled invariant are presented. Finally, having established this necessary theoretical background, a method of constructing nondecreasing sequences of admissible controlled invariant sets with complexity specifications is established

Invariant set computation for constrained uncertain discrete-time linear systems

In this article a novel approach to the determination of polytopic invariant sets for constrained discrete-time linear uncertain systems is presented. First, the problem of stabilizing a prespecified initial condition set in the presence of input and state constraints is addressed. Second, the problem of computing an estimate of the maximal positively invariant or controlled invariant set for this class of systems is investigated. An illustrative example, showing the effectiveness of the proposed methods, is presented

Stability, positive invariance and design of constrained regulators for networked control systems

In this article, the stability analysis, the positive invariance of polyhedral sets and the design of state-feedback regulators for networked control systems (NCS) with bounded transmission delays, constant and unknown or time-varying, are investigated. The dynamics of the NCS is described by autoregressive-moving-average (ARMA) models. Contrary to former approaches based on quadratic Lyapunov functions, in this article polyhedral Lyapunov functions are used for both stability and positive invariance analysis and state-feedback synthesis. Then, based on the property that the exponential of a matrix can be expressed as a weighted sum of its constituent matrices, it is proven that the problems of determination of stability margins or the design of stabilising controllers can be reduced to linear programming optimisation problems. The use of ARMA models allows the development of methods for the design of state-feedback controllers satisfying state constraints or convergence rate specifications defined on the NCS state space and not on the state of an augmented state space representation

Stabilization of bilinear continuous-time systems

In this paper, the stabilization problem of continuous-time bilinear systems by linear state-feedback control is investigated. First, conditions guaranteeing the positive invariance of polyhedral sets with respect to quadratic autonomous nonlinear systems are established. Then these results are used for the determination of linear state-feedback constrained and unconstrained control laws making a prespecified polyhedral set domain of attraction of the resulting closed-loop system

A fault detection scheme based on controlled invariant sets for multisensor systems

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Controlled invariance-based fault detection for multisensory control systems

International audienceIn this study, set theoretic methods are used to design a fault-tolerant scheme for a multisensor control application. The basic principle is the separation of the invariant sets for the estimations of the state and tracking error under healthy and faulty functioning. The fault scenario assumes abrupt changes of the observation equations. The main contribution of this paper is the introduction of controlled invariant sets in the fault detection mechanism. The control action is chosen in order to guarantee the closed-loop positive invariance of a candidate region when the exogenous signals (additive disturbances, noise and reference/set-points) are bounded

Cyclic invariance for discrete time-delay systems

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