In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied...

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

We study stochastic elliptic PDEs driven by multiplicative Gaussian white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an e ective tool to study such equations and present the corresponding solvability results.

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...

The aim of this paper is to present algebraic method which is called Wu's method to solving fuzzy complex systems of linear equations. Wu's method is used as a solution procedure for solving the crisp polynomial equations system. This algorithm leads to solving characteristic sets that are amenable to easy solution. To illustrate the easy application of the proposed method, numerical examples a...

We study the integrable discretization of coupled dispersionless equations. Two semi-discrete version and one full-discrete system are given via Hirota's bilinear method. Soliton solutions for derived discrete systems also presented.