survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

boundary feedback control in networks of open channels this article deals with the regulation of water flow in open channels modelled by saint venant equations by means of a riemann invariants approach we deduce stabilizing control laws for a single horizontal reach without friction the stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies a control law design based on this condition is illustrated with a simple case study two reaches in cascade the proof of the main stability theorem is based on a previous result from li ta tsien concerning the existence and decay of classical solutions of hyperbolic systems

stability of switched linear hyperbolic systems by lyapunov techniques switched linear hyperbolic partial differential equation sa re considered in this technical note they model infinite dimensional systems of conservation laws and balance laws which are potentially affecte db y a distributed source or sink term the dynamics and the boundary condi tions are subject to abrupt changes given by a switching signal modeled as a piecewise constant function and possibly a dwell time by means of lyapunov techniques some sufficient conditions are obtained for the expo nential stability of the switching system uniformly for all switching signals different cases are considered with or without a dwell time assumption on the switching signals and on the number of positive characteristic veloci ties which may also depend on the switching signal some numerical sim ulations are also given to illustrate some main results and to motivate this study

dynamic triggering mechanisms for event triggered control in this technical note we present a new class of event triggering mechanisms for event triggered control systems this class is characterized by the introduction of an internal dynamic variable which motivates the proposed name of dynamic event triggering mechanism the stability of the resulting closed loop system is proved and the influence of design parameters on the decay rate of the lyapunov function is discussed for linear systems we establish a lower bound on the inter execution time as a function of the parameters the influence of these parameters on a quadratic integral performance index is also studied some simulation results are provided for illustration of the theoretical claims

switching rules for stabilization of linear systems of conservation laws in this paper the exponential convergence in l 2 norm is analyzed for a class of switched linear systems of conservation laws the boundary conditions are subject to switches we investigate the problem of synthesizing stabilizing switching controllers by means of lyapunov techniques three control strategies are developed based on steepest descent selection possibly combined with a hysteresis and a low pass filter for the first strategy we show the global exponential stabilizability but no result for the existence and uniqueness of trajectories can be stated for the other ones the problem is shown to be well posed and global exponential convergence can be obtained moreover we consider the robustness issues for these switching rules in presence of measurement noise some numerical examples illustrate our approach and show the merits of the proposed strategies particularly we have developed a model for a network of open channels with switching controllers in the gate operations

a new approach to the solution of the l sub 1 control problem the scaled q method we explore an approach for solving multiple input multiple output mimo l sub 1 optimal control problems this approach which we refer to as the scaled q approach is introduced to alleviate many of the difficulties facing the numerical solution of optimal l sub 1 control problems in particular the computations of multivariable zeros and their directions are no longer required the scaled q method also avoids the pole zero cancellation difficulties that existing methods based on zero interpolation face when attempting to recover the optimal controller from an optimal closed loop map because the scaled q approach is based on solving a regularized auxiliary problem for which the solution is always guaranteed to exist it can be used no matter where the system zeros are including the stability boundary upper and lower bounds that converge to the optimal cost are provided and all solutions are based on finite dimensional linear programming for which efficient software exists

non minimal factorization approach to the l gain of discrete time linear systems a method is presented to compute the gain of discrete time linear mimo systems which is based on a newly derived sequence of factorizations for g z by resorting to a chain scattering representation of the system the proposed approach offers a criterion enabling one to cope with the static output feedback 1 control design by solving a finite set of linear inequalities numerical examples are reported as well as an application to the synthesis of a performing decentralized 1 controller

technical communique optimization based design of fixed order controllers for command following for discrete time scalar systems we propose an approach for designing feedback controllers of fixed order to minimize an upper bound on the peak magnitude of the tracking error to a given command input the work makes use of linear programming to design over a class of closed loop systems recently proposed for the rejection of non zero initial conditions and bounded disturbances we incorporate performance robustness in the form of a guaranteed upper bound on the peak magnitude of the tracking error under plant coprime factor uncertainty

a convex optimization approach to fixed order controller design for disturbance rejection in siso systems the problem of rejection of persistent unknown but bounded disturbances can be solved using the well known l sup 1 design approach however in spite of its success this theory suffers from the fact that the resulting controller may have arbitrarily high order even in the state feedback case in addition system performance is optimized under the assumption of zero initial conditions in this paper we propose a new approach to the problem of synthesizing fixed order controllers to optimally reject persistent disturbances the main result of the paper shows that this approach leads to a finite dimensional convex optimization problem that can be efficiently solved

small gain theorems for large scale systems and construction of iss lyapunov functions we consider interconnections of n nonlinear subsystems in the input to state stability iss framework for each subsystem an iss lyapunov function is given that treats the other subsystems as independent inputs a gain matrix is used to encode the mutual dependencies of the systems in the network under a small gain assumption on the monotone operator induced by the gain matrix a locally lipschitz continuous iss lyapunov function is obtained constructively for the entire network by appropriately scaling the individual lyapunov functions for the subsystems the results are obtained in a general formulation of iss the cases of summation maximization and separation with respect to external gains are obtained as corollaries

l l gain analysis for positive linear systems with unbounded time varying delays this technical note addresses the l gain respectively l gain analysis problem for discrete time respectively continuous time positive linear systems with unbounded time varying delays for the discrete time case by virtue of the monotonicity of an auxiliary system and the corresponding delay free system it is shown that the l gain of discrete time positive systems with unbounded delays is insensitive of the magnitude of delays for the continuous time case we first construct a sampled data positive system and analyze its monotonicity and asymptotic behavior then by comparing the delayed positive system with the proposed sampled data positive system and the corresponding delay free system it is further proved that the l gain of continuous time positive systems with unbounded delays is also independent of the delays and fully determined by the system matrices the application of the results is illustrated by a sampled data system with unbounded sampling intervals

mimo l 1 optimal control problems via the polynomial equations approach the general mimo multi block l 1 optimal control problem is considered a novel solution is derived by resorting to polynomial techniques and simple algebraic conditions on the free parameter of the yjbk parameterization as a result we arrive at unconstrained lp formulations less affected by redundancy and solvable by standard lp solvers as usual because the optimal controller is in general infinite dimensional a solution scheme based on solving sequences of increasing larger finite dimensional sub super optimal optimization problem is proposed viz sequences of finite dimensional optimization problems whose solutions provide lower and respectively upper bounds to the optimum monotonically converging to it finally an example is presented in order to exemplify the theory and show the effectiveness of the method

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

on computing the worst case peak gain of linear systems based on the bounds due to doyle and boyd we present simple upper and lower bounds for the l1 norm of the tail of the impulse response of finite dimensional discrete time linear time invariant systems using these bounds we may in turn compute the l gain of these systems to any desired accuracy by combining these bounds with results due to khammash and pearson we derive upper and lower bounds for the worst case l gain of discrete time systems with diagonal perturbations

gas flow in fan shaped networks classical solutions and feedback stabilization we analyze the subcritical gas flow through fan shaped networks of pipes that is through tree shaped networks with exactly one node where more than two pipes meet the gas flow in pipe networks is modeled by the isothermal euler equations a hyperbolic pde system of balance laws for this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval furthermore we present a lyapunov function and boundary feedback laws to stabilize a fan shaped network around a given stationary state

robust stability analysis of nonlinear discrete time systems with application to mpc the regional input to state stability of nonlinear possibly discontinuous discrete time systems is studied under the assumption that the equilibrium of the corresponding nominal model is asymptotically stable the obtained results are used for the synthesis of a nominal model predictive control law ensuring inherent robustness a numerical example is reported that witnesses the effectiveness of the approach

local exponential h2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping in this work we consider the problem of boundary stabilization for a quasilinear 2 times2 system of first order hyperbolic pdes we design a new full state feedback control law with actuation on only one end of the domain which achieves h 2 exponential stability of the closed loop system our proof uses a backstepping transformation to find new variables for which a strict lyapunov function can be constructed the kernels of the transformation are found to verify a goursat type 4 times4 system of first order hyperbolic pdes whose well posedness is shown using the method of characteristics and successive approximations once the kernels are computed the stabilizing feedback law can be explicitly constructed from them

event based control of linear hyperbolic systems of conservation laws in this article we introduce event based boundary controls for 1 dimensional linear hyperbolic systems of conservation laws inspired by event triggered controls developed for finite dimensional systems an extension to the infinite dimensional case by means of lyapunov techniques is studied the main contribution of the paper lies in the definition of two event triggering conditions by which global exponential stability and well posedness of the system under investigation is achieved some numerical simulations are performed for the control of a system describing traffic flow on a roundabout

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback the objective of this note is to propose a dynamic output control scheme within the lmi framework for robust decentralized stabilization of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints the procedure utilizes the general linear dynamic feedback structure and consists of two steps the first giving a block diagonal lyapunov matrix together with the robustness degree and the second the controller parameters a numerical example illustrates the applicability of the method