global stabilization for a class of switched nonlinear feedforward systems abstract the problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper based on the integrator forwarding technique and the common lyapunov function method we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed loop system a common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

closed loop stabilization of planar bilinear switched systems in this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1 we construct a class of state static memoryless stabilizing feedback laws which preserve the properties of open loop switching signals in order to prove the stability of the implemented system we use lyapunov techniques for differential equations with discontinuous righthand side finally we point out some possible extensions of our result and compare it with related results previously proven by other authors

on switching h controllers for a class of linear parameter varying systems abstract we consider switching h controllers for a class of linear parameter varying lpv systems scheduled along a measurable parameter trajectory the candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable we provide sufficient conditions to guarantee the stability of the switching lpv systems in terms of the dwell time and the average dwell time our results are illustrated with an example where switching between two robust controllers is performed for an lpv system

on switching stabilizability for continuous time switched linear systems this technical note studies switching stabilization problems for continuous time switched linear systems we consider four types of switching stabilizability defined under different assumptions on the switching control input the most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time varying system is asymptotically stable discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length in addition we define feedback stabilizability in filippov sense respectively sample and hold sense as the existence of a feedback law under which closed loop filippov solution respectively sample and hold solution is asymptotically stable it is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions

totally geodesic submanifolds of the complex and the quaternionic 2 grassmannians in this article the totally geodesic submanifolds in the complex 2 grassmannian g 2 c n 2 and in the quaternionic 2 grassmannian g 2 h n 2 are classified it turns out that for both of these spaces the earlier classification of maximal totally geodesic submanifolds in riemannian symmetric spaces of rank 2 published by c hen and n a g ano 1978 is incomplete for example g 2 h n 2 with n 5 contains totally geodesic submanifolds isometric to a hp 2 its metric scaled such that the minimal sectional curvature is 1 5 they are maximal in g 2 h 7 g 2 c n 2 with n 4 contains totally geodesic submanifolds which are isometric to a cp 2 contained in the hp 2 mentioned above they are maximal in g 2 c 6 neither submanifolds are mentioned by chen and nagano

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

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

bounds for blow up time in a semilinear parabolic problem with viscoelastic term abstract we consider a semilinear parabolic equation with viscoelastic term u t u 0 t g t s u x s d s u p 2 u by the means of differential inequality technique we obtain a lower bound for blow up time of the solution if blow up occurs at the same time we establish a new blow up criterion and give an upper bound for blow up time of the solution under some conditions on p g and u 0

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

blow up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions this paper is concerned with the blow up of the solution to a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions lower bound for blow up time is derived when the blow up does occur

extended invariance principle for nonautonomous switched systems stability analysis is developed for nonlinear nonautonomous switched systems trajectories of which admit generally speaking a nonunique continuation on the right for these systems krasovskii lasalle s invariance principle is extended in such a manner to remain true even in the nonautonomous case in addition to a nonsmooth lyapunov function with negative semidefinite time derivatives along the system trajectories the extended invariance principle involves a coupled indefinite function to guarantee asymptotic stability of the system in question as an illustration of the capabilities of this principle a switched regulator of a fully actuated manipulator with frictional joints is constructed

necessary and sufficient conditions for regional stabilisability of second order switched linear systems with a finite number of subsystems in this paper the switching stabilisation problem of second order switched linear systems is studied by extending the best case switching signal bcss criteria for second order switched linear systems with two subsystems to the general case with any finite number of subsystems necessary and sufficient conditions for regional stabilisability of second order switched linear systems with any finite number of subsystems are proposed in this paper the main idea of this paper is to divide all the subsystems in a region into two groups based on their trajectory directions in that region by comparing pairwise the most stable subsystem for each group in a region can be determined and the bcss analysis among all the subsystems in that region is reduced to the bcss analysis between the two most stable subsystems in that region

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

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

global stabilisation of switched nonlinear systems in p normal form with mixed odd and even powers this article investigates the problem of global stabilisation for a class of switched nonlinear systems in p normal form whose subsystems are not assumed to be asymptotically stabilisable unlike the existing results on systems in p normal form where the power order is only positive odd integer we allow positive even integer of the power order using the convex combination method and the adding a power integrator technique we construct a switching law and design state feedback controllers of individual subsystems explicitly by a recursive design algorithm to guarantee asymptotic stability of the closed loop system the designed method is also extended to the global stabilisation problem of switched nonlinear systems in p normal form with zero dynamics as an application of the proposed design method a continuously stirred tank reactor is studied

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

blow up phenomena for some nonlinear parabolic problems abstract we consider the blow up of solutions of equations of the form u t div u 2 grad u f u by means of a differential inequality technique a lower bound for blow up time is determined if blow up does occur as well as a criterion for blow up and conditions which ensure that blow up cannot occur

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

technical communique switched state feedback control for continuous time uncertain systems this paper is concerned to design a switched state feedback robust control for continuous time systems subject to norm bounded uncertainty as important features of the proposed design method we mention that it can handle a general lft structure for the uncertainty and it is based on stability conditions that can be numerically solved by means of lmis and a line search moreover the switching rule as well as the state feedback gains are determined from the minimization of a guaranteed cost function derived from a multi objective criterion the theoretical results are illustrated with an academic example

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

exponential stabilization of discrete time switched linear systems this article studies the exponential stabilization problem for discrete time switched linear systems based on a control lyapunov function approach it is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control lyapunov function such a converse control lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic lyapunov functions for convenience or heuristic reasons in addition it is also proved that if a switched linear system is exponentially stabilizable then it must be stabilizable by a stationary suboptimal policy of a related switched linear quadratic regulator lqr problem motivated by some recent results of the switched lqr problem an efficient algorithm is proposed which is guaranteed to yield a control lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

lower bounds for blow up time in parabolic problems under dirichlet conditions we consider an initial boundary value problem for the semilinear heat equation whose solution may blow up in finite time we use a differential inequality technique to determine a lower bound on blow up time if blow up occurs a second method based on a comparison principle is also presented

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

technical communique stabilizing controllers design for switched nonlinear systems in strict feedback form this paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching based on the backstepping method and the control lyapunov function approach it is shown that under a simultaneous domination assumption a switched nonlinear system in strict feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller a universal formula for constructing stabilizing feedback laws is presented one example is included for verifying the obtained results

on the stabilizability of discrete time switched linear systems novel conditions and comparisons in this paper we deal with the stabilizability property for discrete time switched linear systems a recent necessary and sufficient characterization of stabilizability based on set theory is considered as the reference for comparing the computation oriented sufficient conditions the classical bmi conditions based on lyapunov metzler inequalities are considered and extended novel lmi conditions for stabilizability derived from the geometric ones are presented that permit to combine generality with computational affordability for the different conditions the geometrical interpretations are provided and the induced stabilizing switching laws are given the relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity

feedback stabilization for multiinput switched nonlinear systems two subsystems case in this note based on the control lyapunov function approach a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived additionally a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold one numerical example is given to illustrate the results

h_ infty control of switched nonlinear systems in p normal form using multiple lyapunov functions the problem of h control of switched nonlinear systems in p normal form is investigated in this technical note where the solvability of the h control problem for individual subsystems is unnecessary using the generalized multiple lyapunov functions method and the adding a power integrator technique we design a switching law and construct continuous state feedback controllers of subsystems explicitly by a recursive design algorithm to produce global asymptotical stability and a prescribed h performance level multiple lyapunov functions are exploited to reduce the conservativeness caused by adoption of a common lyapunov function for all subsystems which is usually required when applying the backstepping like recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

exponential stability with l_ 2 gain condition of nonlinear impulsive switched systems in this technical note we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time varying disturbances by using the switched lyapunov function method sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained they ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the l2 gain condition based on the stability results obtained an effective computational method is devised for the construction of switched linear stabilizing feedback controllers a numerical example is presented to illustrate the effectiveness of the results obtained

hybrid state feedback stabilization with l 2 performance for discrete time switched linear systems in this paper the co design of continuous variable controllers and discrete event switching logics both in state feedback form is investigated for a class of discrete time switched linear control systems it is assumed that none of the subsystems is stabilized through a continuous state feedback alone however it is possible to stabilize the whole switched system via carefully designing both the continuous controllers and the switching logics sufficient synthesis conditions for this co design problem are proposed here in the form of bilinear matrix inequalities which is based on the argument of multiple lyapunov functions the closed loop switched system forms a special class of linear hybrid system and is shown to be asymptotically stable with a finite l 2 induced gain

lower bounds for blow up time in a nonlinear parabolic problem abstract for a parabolic problem with a gradient nonlinearity which was introduced by chipot and weissler m chipot f b weissler some blow up results for a nonlinear parabolic problem with a gradient term siam j math anal 20 1989 886 907 see also b kawohl l a peletier observations on blow up and dead cores for nonlinear parabolic equations math z 202 1989 207 217 the question of blow up is investigated specifically if the solution blows up a lower bound for the time of blow up is derived

on stabilizability of switched positive linear systems under state dependent switching this paper addresses the stabilization of switched positive linear systems by state dependent switching we show that if there is a hurwitz convex or linear combination of the coefficient matrices then the switched positive linear system can be exponentially stabilized by means of a single linear co positive lyapunov function if there is not a stable combination of system matrices it is shown that the exponential stabilizability is equivalent to a completeness condition on the coefficient matrices when the switched positive systems can not be stabilized by the single lyapunov function we provide a unified criterion for piecewise exponential stabilizability in terms of multiple linear co positive lyapunov functions

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

stabilisation of second order lti switched positive systems the stabilisation problem of second order switched positive systems consisting of two unstable subsystems is considered in this article by considering the vector fields and geometric characteristics a necessary and sufficient condition for the stabilisability of second order switched positive systems with two unstable subsystems is provided furthermore it is shown via this condition that neither second order switched positive systems consisting of two subsystems with unstable nodes nor second order switched positive systems consisting of one subsystem with unstable nodes and the other with a saddle point can be stabilised via any switching law

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

finite valued feedback laws and piecewise classical solutions abstract often in engineering literature we find control systems in which the open loop inputs are piecewise constant and take values in a finite set such open loop inputs cause the system to have fairly regular solutions on the other hand when acting in closed loop feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type in fact pathological behaviours such as the accumulation of discontinuities may appear zeno phenomenon we give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours

blow up time estimate for a degenerate diffusion equation with gradient absorption this paper deals with a degenerate nonlinear diffusion equation with gradient absorption we at first determine finite time blow up of solutions both in the l norm and an integral measure and then estimate a lower bound of the blow up time by using the differential inequality technique it is mentioned that the blowing up of solutions to nonlinear pdes is usually defined in the l norms while the lower bounds of blow up time are all determined via some measures in the form of energy integrals so in general to estimate the lower bounds of blow up time it has to be assumed that the solutions do blow up in finite time with the involved integral measure before establishing their lower bounds of blow up time such assumptions are unnecessary in this paper

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

state feedback control of switched linear systems an lmi approach this paper addresses the problem of state feedback control of continuous time switched linear systems with arbitrary switching rules a quadratic lyapunov function with a common matrix is used to derive a stabilizing switching control strategy that guarantees i the assignment of all the eigenvalues of each linear subsystem inside a chosen circle in the left hand half of the complex plane ii a minimum disturbance attenuation level for the closed loop switched system the proposed design conditions are given in terms of linear matrix inequalities that encompass previous results based on quadratic stability conditions with fixed control gains although the quadratic stability based on a fixed lyapunov matrix has been widely used in robust control design the use of this condition to provide a convex design method for switching feedback gains has not been fully investigated numerical examples show that the switching control strategy can cope with more stringent design specifications than the fixed gain strategy being useful to improve the performance of this class of systems

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check