The paper is devoted to the state estimation problems for control systems described by nonlinear differential equations with quadratic nonlinearity. The initial state is assumed to be unknown but bounded with given bounds. We present the ellipsoidal techniques which provide the ellipsoidal estimates of reachable sets of this nonlinear control problem. AMS Subject Classification: 93B03, 93C10, 9...

We study the existence and concentration of positive solutions for the quasilinear elliptic equation −ε2u′′ − ε2(u2)′′u + V (x)u = h(u) in R as ε → 0, where the potential V : R → R has a positive infimum and inf∂Ω V > infΩ V for some bounded domain Ω in R, and h is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

In this article, we study the existence of infinitely many solutions for the semilinear elliptic equation −∆u+a(x)u = f(x, u) in a bounded domain of RN (N ≥ 3) with the Dirichlet boundary conditions, where the primitive of the nonlinearity f is either superquadratic at infinity or subquadratic at zero.

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation −∆u = f(u) in the whole R , where f ∈ C(R) is a general nonlinearity and N ≥ 1 is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...

In this paper, we present a novel method for the robust control problem of uncertain nonlinear discrete-time linear systems with sector and slope restrictions. The nonlinear function considered in this paper is expressed as convex combinations of sector and slope bounds. Then the equality constraint is derived by using convex properties of the nonlinear function. A stabilization criterion for t...

In this Letter, we propose new criteria for asymptotic stability of Lur’e systems with sector and slope restrictions. The criteria are expressed in terms of linear matrix inequality which has full block scaling matrix. By interpreting the criteria in the frequency domain using KYP lemma, the less conservativeness of the proposed analysis method is investigated. Furthermore, we analyze the dynam...

The results on well-posedness of two inverse problems with integral overdetermination a bounded interval for class odd-order evolution equations general nonlinearity are established. Either the right-hand side or boundary data chosen as controls. Assumptions smallness input time required.

In this paper a procedure is presented for deriving parameters bounds in SISO Wiener models when the nonlinear block can be modeled by a polynomial and the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear block are tightly bounded. Next in order to estimate the parameters of the linear block, the evaluation of the inner unmeasurable...