Based on the concept of sliding mode control, we study the problem of steady state covariance assignment for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. By suitably using Ito calculus, the controller u(t) can be designed to force the feedback gain matrix G to achieve the...

In this paper, the class of bilinear systems subjected to unknown inputs for which there exists a disturbance decoupled observer with linear error dynamics is characterised. It is shown that the design of this kind of observer is equivalent to the design of a disturbance decoupled observer for a linear system. This result simplifies considerably the observer design comparatively to those propos...

There are a number of applications in which linear noise models are inappropriate. In this paper, the use of bilinear noise modela in circuits and devices is considered. Several physical problems are studied in this framework. These include circuils involving varying parameters (such as variable resistance circuits constructed using Jieldeffect transistors), the effect of switching jitter on sa...

In this paper, the purpose is to design a filter for a stochastic bilinear system which satisfies an H∞ prescribed norm constraint and such that the estimation error is mean-square stable. The system under consideration is bilinear in control input and is subjected to multiplicative noise in both the state and the measurement equations. The system is also corrupted by deterministic perturbation...

A bilinear dynamical system can be used to represent the model of a network in which the state obeys linear dynamics and the input is the edge weight of certain controlled edges in the network. We present algebraic and graph-theoretic conditions for the structural controllability of a class of bilinear systems with a single control where the input matrix is rank one. Subsequently, we use these ...

In this contribution a numerical method for deriving an approximate input-output linearizing controller for minimum phase systems is presented. The approach is based on the derivation of a bilinear approximation model of higher order, which approximates the considered system on a prespecified multivariable state-space interval. By means of the exact input-output linearizing state feedback of th...

Abstract. For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of L...

Using the second flow the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota’s bilinear representation for both flows and combine them toget...

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.