Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems

It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature

Attaining mean square boundedness of a marginally stable noisy linear system with a bounded control input

We construct control policies that ensure bounded variance of a noisy marginally stable linear system in closed-loop. It is assumed that the noise sequence is a mutually independent sequence of random vectors, enters the dynamics affinely, and has bounded fourth moment. The magnitude of the control is required to be of the order of the first moment of the noise, and the policies we obtain are simple and computable.Comment: 10 page

Finite Gain Stabilization of Discrete-Time Linear Systems Subject to Actuator Saturation

It is shown that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain l p stabilization can be achieved by linear output feedback, for all p 2 (1; 1]. An explicit construction of the corresponding feedback laws is given. The feedback laws constructed also result in a closed-loop system that is globally asymptotically stable, and in an input-to-state estimate. Key Words : input saturation, discrete-time linear systems, finite gain stability, Lyapunov functions. 1 Introduction In this paper, we consider the problem of global stabilization of a discrete-time linear system subject to actuator saturation: P : ae x + = Ax + Boe(u + u 1 ); x 2 R n ; u 2 R m y = Cx+ u 2 ; y 2 R r (1) (we use the notation x + to indicate a forward shift, that is, for a function x and an integer t, x + (t) is x(t+1)), where u 1 2 R m is the actuator disturbance, u 2 2 R r is the sensor noise, and oe : R m ! R m represents actuator saturation, i.e..