reachability realization and stabilizability of switched linear discrete time systems abstract in this paper the reachability realization of a switched linear discrete time system which is a collection of linear time invariant discrete time systems along with some maps for switching among them is addressed the main contribution of this paper is to prove that for a switched linear discrete time system there exists a basic switching sequence such that the reachable controllable state set of this basic switching sequence is equal to the reachable controllable state set of the system hence the reachability controllability can be realized by using only one switching sequence we also discuss the stabilizability of switched systems and obtain a sufficient condition for stabilizability two numeric examples are given to illustrate the results

on reachability and stabilization of switched linear systems reachability and stabilization issues for switched linear control systems are addressed a necessary and a sufficient condition are presented for reachability under mild assumptions we prove that the switched linear control systems are stabilizable in addition we show that an element driven switching stabilization strategy can be explicitly constructed

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

controllability of switched time delay systems under constrained switching different from the existing mathematical models for switched systems where the switching from one subsystem to another subsystem is finished instantly in this paper it is assumed that the switching is a transfer process moreover there exists a basic transfer subsystem such that in the transfer process the transfer subsystem is active based on the model of switched systems under constrained switching this paper studies the controllability of such systems with time delay in the control function a necessary and sufficient condition for controllability of such systems is established finally an example is given to illustrate the utility of our results

brief paper a full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs this paper studies open loop stabilization problem for bimodal systems with continuous vector field it is based on the earlier work of the authors on the controllability problem for the same class of systems a full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions it is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case

on controllability of switched linear systems in this paper the controllability of a switched linear system which is a collection of linear time invariant systems along with some maps for switching among them is addressed first a controllable state set is defined as a basic tool to discuss the controllability condition next it is proved that the controllability of a multi input system is equivalent to that of a single input system finally a sufficient and necessary condition for controllability of third order systems is presented according to the proof of this criterion we state a conjecture on the controllability condition of n dimensional systems a numeric example is given to illustrate the result

brief paper on partitioned controllability of switched linear systems when a switched linear system is not completely controllable the controllability subspace is not enough to describe the controllability of the system over whole state space in this case the state space can be divided into two or three control invariant sub manifolds which form a control related partition of the state space this paper investigates when each component is a controllable sub manifold first we consider when a sub manifold is controllable for no control input case then the results are used to produce a necessary and sufficient condition assuring the controllability of the partitioned control invariant sub manifolds of a class of switched linear systems an example is given to demonstrate the effectiveness of the results

necessary and sufficient conditions for stabilization of discrete time planar switched systems abstract this paper discusses the stabilization problem for single input discrete time planar switched systems we establish necessary and sufficient conditions for the stabilization of planar switched systems a series of linear inequalities are presented for describing the set of all common quadratic lyapunov functions our results are not only easily testable but also constructive

stabilizability and insensitivity of switched linear systems this note identifies two types of stabilizability for switched systems the pointwise stabilizability and the consistent stabilizability necessary conditions and sufficient conditions for both types are presented for switched linear systems insensitivity issues are briefly addressed as well

controllability of timed continuous petri nets with uncontrollable transitions this paper is concerned with controllability of timed continuous petri nets under infinite server semantics with uncontrollable transitions which are a class of hybrid systems piecewise linear this class of hybrid systems is suitable for representing biological systems high traffic information networks heavily loaded supply chains etc by adopting a control theory approach the contribution of this paper is the characterisation of controllability over sets of equilibrium markings potential equilibrium points first inside a single marking region or linear mode and later extended to several regions

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

reachability conditions for switched linear singular systems the reachability problem of switched linear singular systems is investigated in this note by using the geometric approach and the admissible control set introduced a necessary condition and a sufficient condition on complete reachability are presented the conditions are the same as those of the conventional nonsingular switched linear systems and normal nonswitching singular systems given in previous papers when the systems degenerate to normal singular systems and conventional switched systems respectively

a general existence theorem for embedded minimal surfaces with free boundary in this paper we prove a general existence theorem for properly embedded minimal surfaces with free boundary in any compact riemannian 3 manifold m with boundary m these minimal surfaces are either disjoint from m or meet m orthogonally the main feature of our result is that there is no assumptions on the curvature of m or convexity of m we prove the boundary regularity of the minimal surfaces at their free boundaries furthermore we define a topological invariant the filling genus for compact 3 manifolds with boundary and show that we can bound the genus of the minimal surface constructed above in terms of the filling genus of the ambient manifold m our proof employs a variant of the min max construction used by colding and de lellis on closed embedded minimal surfaces which were first developed by almgren and pitts 2014 wiley periodicals inc

stabilization of switched linear systems with time delay in detection of switching signal a feedback stabilization problem for switched linear systems with time delay in detection of switching signal is formulated first online state feedback controller design method for asymptotic stability and exponential stability is given then offline state feedback controller design method for asymptotic stability and exponential stability is given as well

reachability and controllability of switched linear discrete time systems this paper investigates the reachability and controllability issues for switched linear discrete time systems geometric characterization of controllability is presented for reversible systems the controllable sets and the reachable sets are identified in wonham s geometric approach and verifiable conditions for reachability and controllability are also presented

brief digital optimal reduced order control of pulse width modulated switched linear systems in this paper digital optimal control of pulse width modulated switched linear systems is considered the equivalent discrete time system and its deviation around a stationary solution plays an important role an optimal linear discrete time deviation controller is developed the controller is chosen to be one step ahead predictive which is a natural choice for control of digital pulse modulated systems the controller is optimal i e a cost criterion is minimized the theory is generally applicable and gives in principle a tool to design a digital optimal controller for an arbitrary pulse width modulated switched linear system the theory is illustrated by examples from the field of switched electrical networks

linear and quasilinear parabolic equations in sobolev space abstract we consider linear parabolic equations of second order in a sobolev space setting we obtain existence and uniqueness results for such equations on a closed two dimensional manifold with minimal assumptions about the regularity of the coefficients of the elliptic operator in particular we derive a priori estimates relating the sobolev regularity of the coefficients of the elliptic operator to that of the solution the results obtained are used in conjunction with an iteration argument to yield existence results for quasilinear parabolic equations

on the controllability of switching linear systems this note presents a necessary and sufficient condition for small time controllability of a linear switching system that is a collection of linear time invariant control systems where a trajectory is any concatenation of trajectories of the individual systems this result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone

closed curve solutions and limit cycles in a class of second order switched nonlinear systems this paper studies the problem of finding the initial states for which the solution of a class of switched systems consisting of unstable second order nonlinear subsystems is convergent a method is described and applied to establish the regions in the plane where it is possible to define a switching law such that the solution of a class of switched nonlinear systems converges to the origin we prove that under certain conditions these regions are delimited by closed curve solutions of the switched system furthermore a sufficient condition for the closed curve solution to be a limit cycle is presented finally a numerical example is included in order to illustrate the results

reachability properties of single input continuous time positive switched systems in this paper two reachability properties for single input positive switched systems are introduced monomial reachability and reachability monomial reachability which represents a necessary but not sufficient condition for reachability is fully characterized necessary and sufficient conditions for reachability are provided for the class of n dimensional systems switching among n subsystems several necessary or sufficient conditions are also provided moreover the definition of k switching reachability set is given and an equivalent condition for the existence of an upper bound on the number of switchings required to reach any reachable vector is given finally it is shown that for reachable systems of low dimension n 2 or n 3 each vector of the positive orthant can be reached by resorting to a switching sequence which switches no more than n 1 times

brief paper periodic stabilizability of switched linear control systems stabilizability via direct observer based state feedback control for discrete time switched linear control systems slcss is investigated in this paper for an slcs the control factors are not only the control input but also the switching signal and they need to be designed in order to stabilize the system as a result stabilization design for slcss is more complicated than that for non switched ones differently from the existing approaches a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems it is highlighted that multiple feedback controllers need to be designed for one subsystem for discrete time slcss it is proved that reachability implies periodic stabilizability via state feedback a necessary and sufficient criterion for periodic stabilizability is also established two stabilization design algorithms are presented for real application moreover it is proved that reachability and observability imply periodic stabilizability via observer based feedback for discrete time slcss periodic detectability as the dual concept of periodic stabilizability is discussed and the stabilization design algorithms via observer based feedback are presented as well

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

monomial reachability and zero controllability of discrete time positive switched systems in this paper monomial reachability and zero controllability properties of discrete time positive switched systems are investigated necessary and sufficient conditions for these properties to hold together with some interesting examples and some testing algorithms are provided

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

controllability and stabilizability of switched linear systems in this paper we study the conjecture made in ieee trans automat control 47 8 2002 1401 concerning the existence of basic switching sequence for switched systems and give it an affirmative answer and a construction method this paper proves that for switched linear system there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system hence the controllability can be realized by using only one switching sequence then the result is extended to the systems with time delay in controls furthermore we define the stabilizability of switched linear systems and based on certain transformation of state coordinate we give a necessary and sufficient condition for the stabilizability two examples are presented to illustrate the obtained results

accessibility of switched linear systems this note considers the controllability of switched linear systems the structure of accessibility lie algebra is revealed some accessibility properties are proved certain necessary and sufficient conditions for local or global weak or normal controllability of a large class of switched linear systems are obtained

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

commuting and stable feedback design for switched linear systems abstract in the paper commuting and stable feedback design for switched linear systems is investigated this problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed loop systems are not only asymptotically stable but also commuting each other a new concept common admissible eigenvector set caes is introduced to establish necessary sufficient conditions for commuting and stable feedback controllers for second order systems a necessary and sufficient condition is established moreover a parametrization of the caes is also obtained the motivation comes from stabilization of switched linear systems which consist of a family of lti systems and a switching law specifying the switching between them where if all the subsystems are stable and commuting each other then the total system is stable under arbitrary switching

technical communique a new perspective on criteria and algorithms for reachability of discrete time switched linear systems the paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete time systems direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability reachability algorithm and kalman type algebraic rank criteria also the existing geometric criteria is simplified and new algebraic conditions on controllability and reachability are given