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Register a new userControllability properties and invariance pressure for linear discrete-time systems
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For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure of this control set is proved.
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This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.
In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the $k$-fold exterior product. As consequence we establish a necessary and sufficient condition for controllability of a class of bilinear control systems.
We are concerned about the controllability of a general linear hyperbolic system of the form $partial_t w (t, x) = Sigma(x) partial_x w (t, x) + gamma C(x) w(t, x) $ ($gamma in mR$) in one space dimension using boundary controls on one side. More precisely, we establish the optimal time for the null and exact controllability of the hyperbolic system for generic $gamma$. We also present examples which yield that the generic requirement is necessary. In the case of constant $Sigma$ and of two positive directions, we prove that the null-controllability is attained for any time greater than the optimal time for all $gamma in mR$ and for all $C$ which is analytic if the slowest negative direction can be alerted by {it both} positive directions. We also show that the null-controllability is attained at the optimal time by a feedback law when $C equiv 0$. Our approach is based on the backstepping method paying a special attention on the construction of the kernel and the selection of controls.
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on L-switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same $L$-switching-cycle. These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. Furthermore, it has been proven that the proposed L-switching-cycle can eventually achieve the nonconservativeness in stability analysis as long as a sufficiently long L-switching-cycle is adopted. A numerical example is provided to illustrate our theoretical results.
In this paper, an attack-resilient estimation algorithm is presented for linear discrete-time stochastic systems with state and input constraints. It is shown that the state estimation errors of the proposed estimation algorithm are practically exponentially stable.
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