stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

event triggered h control for discrete time piecewise affine systems with norm bounded uncertainties this paper is concerned with the problem of designing event triggered h controllers for discrete time piecewise affine pwa systems with norm bounded uncertainties event triggered scheme transmi

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems in this article the regional stabilisability issues of a pair of planar lti systems are investigated through the geometrical approach and easily verifiable necessary and sufficient conditions are derived the main idea of the article is to characterise the best case switching signals based upon the variations of the constants of the integration of the subsystems the conditions are generic as all possible combinations of the subsystem dynamics are considered

partial differential equations from integrable vertex models in this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations this mechanism is illustrated for the uq sl 2 invariant six vertex model and the resulting partial differential equation is studied for particular values of the lattice length

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

passivity and absolute stabilization of a class of discrete time nonlinear systems abstract by using the theory of discrete time passive systems and the concept of feedback equivalence we present an approach toward deriving sufficient conditions for the global stabilization of discrete time nonlinear systems in the form x k 1 tf x k g x k u k the central feature of the approach is that a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature

rough surface scattering via the smoothing method the smoothing method is used to find the first two moments i e the mean and the two point two time correlation function of the field scattered by a rough surface the results are expressed in terms of a reflection coefficient and a differential scattering coefficient they are compared with those found by several other methods

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

computation of lyapunov functions for smooth nonlinear systems using convex optimization linearly parameterized non quadratic lyapunov functions for smooth nonlinear systems are computed numerically using large scale linear or quadratic programming

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

observer based control of discrete time lipschitzian non linear systems application to one link flexible joint robot the problem of designing asymptotic observers along with observer based feedbacks for a class of discrete time non linear systems is considered we assume that the system non linearity is globally lipschitz and the system is supposed to be stabilizable by a linear controller sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states a numerical example of a single link flexible joint robot is presented to illustrate the efficacy of the theoretical developments

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems