lyapunov iterations for optimal control of jump linear systems at steady state in this paper we construct a sequence of lyapunov algebraic equations whose solutions converge to the solutions of the coupled algebraic riccati equations of the optimal control problem for jump linear systems the obtained solutions are positive semidefinite stabilizing and unique the proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced order decoupled lyapunov equations several examples are included to demonstrate the procedure

on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control abstract existence of maximal solution is proved for a generalized version of the well known standard algebraic riccati equations which arise in certain stochastic optimal control problems

complete results for a class of state feedback disturbance attenuation problems the author considers a problem of disturbance attenuation using full state feedback the particular class of linear systems under consideration is closely related to the one block problem in h sup infinity control the author gives a complete solution to this problem in terms of a certain algebraic riccati equation

on the newtonkleinman method for strongly stabilizable infinite dimensional systems we consider the newtonkleinman method for strongly stabilizable infinite dimensional systems under certain assumptions the maximal self adjoint solution to the associated control algebraic riccati equation is constructed the constructed solution is also the maximal solution to the corresponding control algebraic riccati inequality

existence and comparison theorems for algebraic riccati equations for continuous and discrete time systems abstract we discuss two comparison theorems for algebraic riccati equations of the form xbr 1 b x x a br 1 c a br 1 c x q c r 1 c 0 simultaneously we give sufficient conditions to obtain the existence of the maximal hermitian solution of a riccati equation from the existence of a hermitian solution of a second riccati equation further similar results are given for discrete algebraic riccati equations

spatial three dimensional secondary instability of compressible boundary layer flows three dimensional linear secondary instability theory is extended for compressible and high mach number boundary layer flows the effect of a small but finite amplitude compressible tollmien schlichting wave on the growth of dimensional perturbations is investigated the focus is on principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environnement the effect of increasing number on the onset growth and shape of eigenfunctions of the subharmonics is assessed and the resulting vortical structure is examined

the solution set of the algebraic riccati equation and the algebraic riccati inequality abstract we present a parametrization of the solution set of the algebraic riccati equation and the algebraic riccati inequality of optimal control where we assume only sign controllability of the underlying system furthermore we characterize the existence of maximal and minimal solutions of both the equation and the inequality by checkable conditions

spectral factorization with imaginary axis zeros abstract we examine the problem of the existence and calculation of hermitian solutions p of a linear matrix inequality corresponding to the spectral factorization of a proper rational spectral density in particular zeros are permitted on the finite imaginary axis or at infinity as part of our construction of solutions we show explicitly that each such imaginary axis eigenvalue either finite or infinite defines a fixed part of all solutions p

secondary instability mechanisms in compressible axisymmetric boundary layers secondary instability mechanisms in compressible axisymmetric boundary layers are analyzed using spectrally accurate mean flow and stability codes results show that subharmonic disturbances are the most dangerous secondary disturbances in an environment with a low to moderate intensity of the primary disturbance the relation between spatial and temporal analyses of the secondary disturbance is explored at mach 1 6 along a flat plate and mach 6 8 along a cone spatial direct numerical simulations are utilized to confirm the quantitative predictions from spatial secondary instability theory

structured doubling algorithms for weakly stabilizing hermitian solutions of algebraic riccati equations in this paper we propose structured doubling algorithms for the computation of the weakly stabilizing hermitian solutions of the continuous and discrete time algebraic riccati equations respectively assume that the partial multiplicities of purely imaginary and unimodular eigenvalues if any of the associated hamiltonian and symplectic pencil respectively are all even and the c dare and the dual c dare have weakly stabilizing hermitian solutions with property p under these assumptions we prove that if these structured doubling algorithms do not break down then they converge to the desired hermitian solutions globally and linearly numerical experiments show that the structured doubling algorithms perform efficiently and reliably

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

the regular indefinite linear quadratic optimal control problem stabilizable case this paper addresses an open problem in the area of linear quadratic optimal control we consider the regular infinite horizon stability modulo a subspace indefinite linear quadratic problem under the assumption that the dynamics are stabilizable our result generalizes previous works dealing with the same problem in the case of controllable dynamics we explicitly characterize the unique solution of the algebraic riccati equation that gives the optimal cost and optimal feedback control as well as necessary and sufficient conditions for the existence of optimal controls

on hermitian solutions of the symmetric algebraic riccati equation the structure of the set of hermitian solutions of the matrix quadratic equation xdx xa a x c 0 is studied under the conditions that c c d is positive semidefinite and a d is stabilizable new features e g nonexistence of the minimal solution appear in contrast with the known case when a d is controllable

an implicit sequential algorithm for solving coupled lyapunov equations of continuous time markovian jump systems in this paper an implicit sequential algorithm is presented for solving coupled lyapunov matrix equations of continuous time markovian jump linear systems first some existing iterative algorithms which can be utilized to solve the coupled lyapunov matrix equations are reviewed and discussed next based on the existing parallel iterative algorithm an implicit sequential algorithm is proposed by using the latest updated information the proposed algorithm fills the current gap of implicit algorithms for solving continuous coupled lyapunov matrix equations it is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive definite solutions of the coupled lyapunov matrix equations if the associated markovian jump system is stochastically stable moreover a necessary and sufficient condition is established for the proposed algorithm to be convergent the algorithm presented in this paper has much better convergence performance than other existing iterative algorithms and requires less storage capacity finally a numerical example is given to show the effectiveness of the proposed algorithm

maximal solution of a certain class of periodic riccati differential equations this paper deals with a generalized version of the well known periodic riccati differential equation which arises in certain optimal filtering problems for linear periodic systems a monotonicity property for symmetric periodic equilibrium solutions is established and it is proved that there exists a maximal symmetric periodic equilibrium solution

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

technical communique solution of the state dependent noise optimal control problem in terms of lyapunov iterations in this paper we present the solution to the algebraic riccati type equation of the state dependent noise linear quadratic optimal control problem in terms of algebraic lyapunov iterations by properly initializing the sequence of algebraic lyapunov iterations we got monotonic convergence from above to the positive definite stabilizing solution of the algebraic riccati type equation the solution that represents the optimal solution to the corresponding optimal control problem the proposed algorithm requires much less computational efforts than those previously used to solve the same problem

horoballs and iteration of holomorphic maps on bounded symmetric domains abstract given a fixed point free compact holomorphic self map f on a bounded symmetric domain d which may be infinite dimensional we establish the existence of a family h 0 of convex f invariant domains at a point in the boundary d of d which generalises completely wolff s theorem for the open unit disc in c further we construct horoballs at and show that they are exactly the f invariant domains when d is of finite rank consequently we show in the latter case that the limit functions of the iterates f n with weakly closed range all accumulate in one single boundary component of d

a structured approximation problem with applications to frequency weighted model reduction the authors consider the problem of finding necessary and sufficient conditions for the existence of a q with no more than k poles in the closed left half plane such that the norm of a certain matrix

some new results on algebraic riccati equations arising in linear quadratic differential games and the stabilization of uncertain linear systems abstract this paper presents some new results on algebraic riccati equations arising in linear quadratic differential games the first result is a uniqueness result for solutions of the riccati equations under consideration the second result is concerned with riccati equations which arise in differential games in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the corresponding solution to the riccati equation will also approach zero

parallel computation of the solutions of coupled algebraic lyapunov equations a parallel algorithm for solving systems of coupled lyapunov equations associated with linear jump parameter systems is introduced the recursive scheme is based on solving independent reduced order lyapunov equations monotonicity of convergence is established

nonnegative solutions of algebraic riccati equations abstract nonnegative hermitian solutions of various types of continuous and discrete algebraic riccati equations are studied the hamiltonian is considered with respect to two different indefinite scalar products for the set of nonnegative solutions the order structure and the topology of the set and the stability of solutions is treated for general hermitian solutions a method to compute the inertia is given although most attention is payed to the classical types arising from lq optimal control theory the case where the quadratic term has an indefinite coefficient is studied as well

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

the general nonstrict algebraic riccati inequality abstract if a b is stabilizable it is well known how to verify the solvability or the existence of positive definite solutions of the nonstrict algebraic riccati inequality ari a x xa xbb x q 0 this paper serves to demonstrate how far it is presently possible to generalize these results if the uncontrollable modes of a b are not restricted we prove a new reduction principle which may be formulated as follows the ari has a solution iff a certain reduced order riccati equation for a stabilizable system a linear equation and a reduced order nonstrict lyapunov inequality corresponding to the uncontrollable modes on the imaginary axis have solutions basically the quadratic riccati inequality is hence reduced to a linear lyapunov inequality we discuss how this principle may be applied to actually check the solvability of the ari as the main motivation for our work we briefly explain the consequences of these results for the general state feedback h optimization problem