robust stability of additively perturbed interconnected systems the concept of generalized block diagonal dominance is used to derive robust stability results for additively perturbed interconnected systems these results characterize the robustness of interconnected systems by putting upper bounds on the spectral norms of the various subblocks of admissible perturbations

an algorithm for robust performance tests based on frequency dependent lmis in this paper an algorithm is introduced for feasibility problems associated with frequency dependent linear matrix inequalities these problems correspond to h 2 or h robust performance tests for a given controller in the face of feedback perturbations to this effect an auxiliary h 2 cost functional is introduced and a sequence of h 2 problems with a single linear constraint is considered in which the h 2 cost functional is kept unchanged while the linear constraints are iteratively modified it is shown that in each step the auxiliary optimal solution moves closer in the sense of a weighted quadratic norm to the target feasible set conditions are also established under which the sequence of solutions to the auxiliary problems yields a solution to the original feasibility problem the method is illustrated by a numerical example corresponding to a h robust performance test for a multivariable system

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

robust synthesis of feedforward compensators the design of a feedforward compensator for robust spl hscr sub spl infin or spl hscr sub 2 performance under structured uncertainty is considered for linear time invariant uncertainty a convex method based on linear matrix inequalities lmis across the frequency variable is given for nonlinear or time varying perturbations and spl hscr sub spl infin performance the design problem is reduced exactly to a state space lmi and extensions to spl hscr sub 2 performance are discussed an example illustrates the application of these techniques to two degree of freedom control design

a linearization algorithm for optimizing control systems subject to singular value inequalities the design of feedback linear multivariable systems subject to inequality constraints frequently leads to nonlinear programming problems involving singular values of matrix transfer functions we present a readily implementable and globally convergent algorithm for solving such problems it exploits the structure inherent in singular values differently than do other existing methods

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

existence conditions for unknown input functional observers this article presents necessary and sufficient conditions for the existence and design of an unknown input functional observer the existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions the existence of the observer does not require the satisfaction of the observer matching condition i e equation 16 in hou and muller 1992 design of observers for linear systems with unknown inputs ieee transactions on automatic control 37 871 875 is not limited to estimating scalar functionals and allows for arbitrary pole placement the proposed observer always exists when a state observer exists for the unknown input system and furthermore the proposed observer can exist even in some instances when an unknown input state observer does not exist

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam

matrix criterion robust linear quadratic control problem this paper studies a robust linear quadratic lq control problem with multiple quadratic performance indices specifically a linear model is assumed to be available for each of a prespecified set of operating points of a system a vector valued quadratic control performance index is given at each operating point it is then desired to find the constant feedback gains of a linear controller to obtain satisfactory control performance over all the operating points this is a realistic case involving the minimization of a vector criterion of vector criteria i e a matrix valued criterion the matrix valued criterion gives insight into standard robust lq design and leads to several related vector minimization problems and to natural procedures for computing a satisfactory non inferior solution to the matrix valued minimization problem

frequency response computation via rational interpolation a simple rational interpolation method is given for estimating a frequency response matrix the method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms when coupled with a pole cancellation method the resulting interpolation algorithm is accurate and efficient the error in this procedure has the form of a modified response matrix which means that the interpolation algorithm can be used to approximate both the response matrix and the error

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

dual criterion stochastic optimal control problem for robustness improvement the solution of the dual criterion linear quadratic stochastic optimal control problem is obtained by following a wiener type of solution procedure a stabilizing solution is guaranteed by parameterizing the controller using the desoer fractional representation approach the dual criterion includes sensitivity and complementary sensitivity weighting terms which provide a means of varying the robustness characteristics of the multivariable system

a control lyapunov function approach to feedback stabilization of logical control networks this paper studies the feedback stabilization problem of k valued logical control networks kvlcns and proposes a control lyapunov function clf approach for this problem first the clf is de

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

vector valued versus scalar valued figures of merit in h feedback system design abstract in this paper we adopt the point of view that the real figure of merit in h feedback systems design is the vector valued performance measure w1s w2t where w1s is the frequency weighted sensitivity function and w2t w2 i s the weighted complementary sensitivity function a compensator c0 is optimal if its induced performance w1s c0 w2t c0 is a minimal element of the set of achievable performances in the w1s w2t plane this set is shown to be convex and the fundamental limitations on achievable feedback performance take the geometric interpretation of a polygon bounding from below this convex set the h theory deals with feedback system performance tradeoffs by lumping the two conflicting objective functions s and t into a scalar valued criterion of the form p p w 1 s p p p w 2 t p 1 p where p p are scalar weighting factors and w1 w2 are frequency dependent weighting functions in this paper we develop strategies for weighting functions and weighting factors selections so as to direct the resulting scalar valued criterion design to a minimal element of the set of achievable performances in the w1s w2t plane if this is possible it appears that a scalar valued criterion is most likely to direct the design toward a performance acceptable from the vector valued criterion point of view if p 2 and w1 w2 are nonoverlapping

on the design of linear multivariable feedback systems via constrained nondifferentiable optimization in h sup infinity spaces the design discussed is of linear lumped time invariant multivariable feedback systems subject to various frequency and time domain performance specifications the approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex nondifferentiable optimization problems these problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular uniformly locally lipschitz continuous functions in r sup n

multivariable gain margin abstract the gain margin for a multivariable system is defined by examining the positive definite hermitian p d h portion of the polar decomposition of a non singular perturbation a in the feedback path the dual result defining the phase margin for a multivariable system has been derived by bar on and jonckheere 1990 by examining the unitary portion of the polar decomposition for non singular perturbations this paper focuses on the multivariable gain margin the main result is an extension of the classical siso concept of gain margin to mimo systems the definition for gain margin presented encompasses both gain reduction and gain amplification tolerance because the measurement is relative to the identity matrix as opposed to zero closed loop stability is guaranteed for all p d h matrices in the feedback path whose gain relative to the identity matrix is less than the gain margin of the system calculation of the gain margin requires solving a constrained optimization problem which is almost

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

on dynamic output feedback compensator design using the riccati equation a simple formula for the design of dynamic output feedback compensators so as to reduce closed loop system sensitivity is given it is obtained by reformulating the compensator design problem as a deterministic linear optimal state regulator problem i e an lqg problem and an appropriate sensitivity reduction interpretation the result is given for siso linear systems

frequency response algorithms for h sub infinity optimization with time domain constraints a very broad framework for control system design is considered that encompasses frequency response methodologies for h sub infinity optimization that solve various aspects of the control design problem and that are less well known that state space methods the focus is on linear programming lawson s algorithm and trefethen s algorithm a modified lawson s algorithm is proposed and related to trefethan s method the modified algorithm is shown to be significantly faster than linear programming and lawson s algorithm it is also shown how to extend the modified lawson s algorithm so as to handle time domain constraints in addition to frequency domain specifications which distinguishes it from other h sub infinity optimization methods some steps are taken toward dealing with time domain constraints within an h sub infinity optimization framework

quantification of uncertainty in transfer function estimation a mixed probabilistic worst case approach abstract in this paper an identification problem is solved which is directed towards the use of the identified model as a basis for robust control design a procedure is presented to identify on the basis of time domain measurement data a reduced order finite impulse response fir model together with an upper bound on the model error of the corresponding transfer function using only minor prior information we assume the measurement data to be contaminated with a stochastic noise disturbance with unknown spectral properties by applying a procedure similar to bartlett s procedure of periodogram averaging in conjunction with a periodic input signal the statistics of the model error asymptotically can be obtained from the data the model error consists of two parts a probabilistic part due to the stochastic noise disturbance and a worst case part due to the unmodelled dynamics the latter is explicitly bounded with a hard error bound while for the former a confidence interval can be specified asymptotically this enables an explicit trade off between undermodelling bias and variance terms the resulting error bound appears to be tight