energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

improved measures of stability robustness for linear state space models in this paper the aspect of stability robustness of linear systems is analyzed in the time domain a bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a lyapunov matrix equation solution the resulting bound is shown to be an improved bound over the ones recently reported in the literature also special cases of the nominal system matrix are considered for which the bound is given in terms of the nominal matrix thereby avoiding the solution of the lyapunov matrix equation examples given include comparison of the proposed approach with the recently reported results

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

on the observability inequalities for exact controllability of wave equations with variable coefficients this paper deals with boundary exact controllability for the dynamics governed by the wave equation with nonconstant coefficients in the principal part subject to dirichlet or neumann boundary controls the observability inequalities are established by the riemannian geometry method under some geometric condition for the dirichlet problem and for the neumann problem respectively next a number of nontrivial examples are presented to verify the observability inequality in particular a counterexample is given without boundary exact controllability where the control is exerted on the whole boundary

robust stability of discrete time systems under parametric perturbations stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable in this paper two methods are presented to estimate the stability robustness region of a linear time invariant discrete time system under multiparameter additive perturbations an inherent difficulty which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region is resolved by transforming the problem to stability of a higher order continuous time system this allows for application of the available results on stability robustness of continuous time systems to discrete time systems the results are also applied to stability analysis of discrete time interconnected systems where the interconnections are treated as perturbations on decoupled stable subsystems

on stability of interval matrices new sufficient and sometimes necessary and sufficient conditions are obtained for schur and hurwitz stability of interval matrices by relying on the concept of connective stability and m matrices the necessity part is broadened to include interval matrices with mixed signs of the off diagonal elements provided the sign patterns follow that of the morishima matrix the obtained results are extended to cover convex combinations of interval matrices

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

wave equation with porous nonlinear acoustic boundary conditions generates a well posed dynamical system we consider a structural acoustic wave equation with nonlinear acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with boundary conditions on the interface we prove wellposedness in the hadamard sense for strong and weak solutions the main tool used in the proof is the theory of nonlinear semigroups we present the system of partial differential equations as a suitable cauchy problem dw dt aw though the operator a is not maximally dissipative we are able to show that it is a translate of a maximally dissipative operator the obtained semigroup solution is shown to satisfy a suitable variational equality thus giving weak solutions to the system of pdes the results obtained i dispel the notion that the model does not generate semigroup solutions ii provide treatment of nonlinear models and iii provide existence of a correct state space which is invariant under the flow thus showing that physical model under consideration is a dynamical system the latter is obtained by eliminating compatibility conditions which have been assumed in previous work on the linear case

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

robust stability bounds on time varying perturbations for state space models of linear discrete time systems the stability robustness of linear discrete time systems in the time domain is addressed using the lyapunov approach bounds on linear time varying perturbations that maintain the stability of an asymptotically stable linear time invariant discrete time nominal system are obtained for both structured and unstructured independent perturbations bounds are also derived assuming that various elements of the system matrix are perturbed dependently the result for the structured perturbation case is extended to the stability analysis of interval matrices

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

deterministic and stochastic robustness measures for discrete systems deterministic and stochastic lyapunov theorems are used to demonstrate the robustness of a stable linear time variant discrete time nominal system to both unknown deterministic and stochastic perturbations time domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system it is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed loop system is known to be stable with a certain degree e g as in the case of linear quadratic optimal control with alpha degree of prescribed stability

a note on robust stability bounds the authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of lyapunov functions results obtained with quadratic and with vector lyapunov functions are compared simple examples are used to illustrate the effects of the choice of functions corresponding majorizations and system decompositions

bosonic realizations ofuq c 1 n abstract we construct explicitly the quantum symplectic affine algebrauq sp 2n using bosonic fields the fock space decomposes into irreducible modules of level 1 2 quantizing the feingold frenkel construction forq 1

robust stability of discrete systems the objective of this paper is to show how to choose a liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time invariant discrete systems the choice is interesting because it is also shown that it provides the largest robustness bounds on non linear time varying perturbations which can be established by either norm like or quadratic liapunov functions by applying the results obtained to large scale systems where the role of perturbations is played by the interconnections among the subsystems the least conservative stability conditions are derived for the overall system which are available in the context of vector liapunov functions and m matrices

higher level representations of the quantum affine algebrauq ŝl 2 abstract we introduce the notion of quantum z algebras for the quantum affine algebra after developing the quantum z algebra we use it to study the quantum affine algebrauq sl 2 and construct bases for each of its higher level modules

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis