A large class of nonlinear phenomena can be described using bilinear systems. Such systems are very attractive since they usually require few parameters, to approximate most nonlinearities (compared to other systems). This paper addresses the problems of bilinear system identicalness using Bayesian inference. The Gibbs sampler is used to estimate the bilinear system parameters, from measurements of the system input and output signals

This paper discusses global asymptotic stabilization of a class of discrete-time bilinear descriptor systems. By means of LaSalle invariant principle and the implicit function theorem, a sufficient condition is presented to guarantee the uniqueness and existence of solution and the global asymptotic stability of the resulting closed-loop systems simultaneously. Finally, the effectiveness of the proposed approach is illustrated by a numerical example

We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one