on the limiting zeros of sampled multivariable systems for time invariant linear systems with single input single output it has been shown 3 that as the sampling period goes to 0 the zeros of the corresponding discrete time system obtained by sampling converge to some specific constant values determined only be the degrees of the finite and the infinite zeros of the original continuous time system it is natural to inquire the extent to which this result may be carried over to the case of multivariable systems in this note it is shown that the result is true also for multivariable systems if the difference among the degrees of infinite elementary divisors of the pencil corresponding to the original continuous system is less than two when the last condition is not satisfied the limiting values of the zeros of the discrete system depend in general not only on the integers cited above but also on system parameters

analysis of chemical kinetic systems over the entire parameter space i the sal nikov thermokinetic oscillator in this series of papers we re examine using recently developed techniques some chemical kinetic models that have appeared in the literature with a view to obtaining a complete description of all the qualitatively distinct behaviour that the system can exhibit each of the schemes is describable by two coupled ordinary differential equations and contain at most three independent parameters we find that even with these relatively simple chemical schemes there are regions of parameter space in which the systems display behaviour not previously found quite often these regions are small and it seems unlikely that they would be found via classical methods in part i of the series we consider one of the thermally coupled kinetic oscillator models studied by sal nikov he showed that there is a region in parameter space in which the system would be in a state of undamped oscillations because the relevant phase portrait consists of an unstable steady state surrounded by a stable limit cycle our analysis has revealed two further regions in which the phase portraits contain respectively two limit cycles of opposite stability enclosing a stable steady state and three limit cycles of alternating stability surrounding an unstable steady state this latter region is extremely small so much so that it could be reasonably neglected in any predictions made from the model

stabilization of discrete system zeros an improved design stabilization of discrete system zeros has been previously achieved by providing a fixed pattern of inter sampling time input which deviates from zero order hold however a fixed non zoh input creates several problems indefinite fluctuation of the system output which causes a deterioration in performance highly fluctuating input which accelerates actuator fatigue and counter acting control which increases demand for input energy in this work zero placement is achieved with a temporary non zoh input this temporary input pattern which converges asymptotically toward a zoh input pattern removes the problems associated with a fixed non zoh input design

analytic study on the intrinsic zeros of sampled data systems this paper investigates the properties of the mapping from the simple zero spl gamma of a scalar continuous time system to the corresponding zero spl gamma t of the sampled data system that results by its discretization using a zero order hold where t is the sampling period it is shown that spl gamma t admits a taylor expansion with respect to t and that it coincides with that of exp spl gamma t at least up to the second order term in general and at least up to the third order term if the relative degree of the continuous time system is greater than or equal to two the result is applied to derive a new stability condition of spl gamma t for sufficiently small sampling periods

properties of zeros in digital control systems with computational time delay abstract a digital control system with computational time delay is considered in which the controlled plant is a continuous time linear system and the control input is calculated by a digital computer based on the data of the output measured before a certain time not greater than the sampling period some qualitative properties of the zeros such as the characteristics of the limiting zeros the parity relation between real poles and zeros and the behaviour of the zeros with respect to the computational time delay are investigated and the parity interlacing property and its dual are derived a method of stabilization by a stable digital compensator using the inter sample data is also proposed finally the first order hold case is discussed

two delay robust digital control and its applications avoiding the problem on unstable limiting zeros in the design of linear control systems the existence of unstable zeros makes it difficult to construct many control systems when the usual digital control scheme is used unstable zeros appear in the discrete time model due to the existence of limiting zeros even though the continuous time plant is minimal phase to avoid this unstable zero problem two new digital control schemes called two delay output control and two delay input control are proposed these control systems are proved to have no finite zeros asymptotic inverse systems pole assignable unknown input observers and output feedback controllers having the ltr loop transfer recovery property are developed using the two delay output control zero assignable control systems and model matching control systems are developed using the two delay input control

on zeros of pulse transfer functions the famous spl aring strom hagander sternby theorem 1984 on limiting zeros of the pulse transfer function is extended by determining the accuracy of the asymptotic results for both the discretization and the intrinsic zeros when the sampling interval is small closed form formulas are derived that express the degree of the principal term of taylor expansion of the difference between the true zeros and asymptotic ones as a function of the relative degree of the underlying continuous time system and the value of the corresponding coefficient itself certain known results on asymptotic zeros are shown to be particular cases of the result presented

the relationship between real poles and real zeros in siso sampled data systems a relationship between real poles and real zeros of siso single input single output sampled data systems is presented which is independent of the sampling period the relation is stated in terms of a parity property involving the number of real zeros between any two real poles this property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling a sufficient condition for stability of a sampled system with a continuous time plant having all real zeros and a sufficient condition for instability of a two sampled system with an unstable plant is developed

a stability condition of zeros of sampled multivariable systems this note derives a new condition for zeros of sampled multivariable systems to be stable for sufficiently small sampling periods it is a natural extension of hagiwara s result for single input single output systems 1993 to multivariable systems

zero dynamics of sampled data models for nonlinear multivariable systems in fractional order hold case the paper is concerned with the properties of approximate sampled data models and their zero dynamics as the sampling period tends to zero composed of a fractional order hold froh a continuous time multivariable plant and a sampler in cascade the emphasis of this paper is the stability of discrete zero dynamics with the generalized gain of the froh where we also present a condition to assure the stability of the sampling zero dynamics which they have no counterpart in the underlying continuous time system of the resulting model similar to the linear case the parameter is the only factor in affecting the stability of discrete zero dynamics and the appropriate is determined to obtain the froh that provides zero dynamics as stable as possible or with improved stability properties even when unstable for a given continuous time multivariable plant the study is also shown that the stability of the sampling zero dynamics is improved compared with a zero order hold zoh

stability of the intersection of solution sets of semi infinite systems many mathematical programming models arising in practice present a block structure in their constraint systems consequently the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not the existence theorems allow to decide when the intersection of non empty sets in the euclidean space which are the solution sets of systems of possibly infinite inequalities is empty or not in those situations where the data i e the constraints can be affected by some kind of perturbations the problem consists of determining whether the relative position of the sets is preserved by sufficiently small perturbations or not this paper focuses on the stability of the non empty empty intersection of the solutions of some given systems which can be seen as the images of set valued mappings we give sufficient conditions for the stability and necessary ones as well in particular we consider semi infinite convex systems and also linear systems in this last case we discuss the distance to ill posedness

comments on zeros of discretized continuous systems expressed in the euler operator an asymptotic analysis with reply in the original paper by tesfaye and tomizuka ibid vol 40 p 743 7 1995 an asymptotic analysis was used to address the zero structure of discretized continuous time systems expressed in the euler or forward difference operator the method was developed for application to multivariable control systems the authors state that the analysis is flawed so that a theorem is true as stated only when the continuous time relative degree is equal to two they indicate how the analysis may be rectified tesfaye and tomizuka acknowledge the error and the correctness of the result in this paper

a limiting property of the inverse of sampled data systems on a finite time interval if one considers a sampled data system derived from a continuous time system with a relative degree of one or two on a finite time interval it is not simple to predict the behavior of the output of the inverse of the sampled data system as the sampling period goes to zero this is because the number of sample points increases while the zeros of the pulse transfer function tend to the boundary between the stable and unstable areas the paper shows that the output of the sampled data inverse systems converges to the output of the continuous time inverse systems independently of the stability of zeros

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

asymptotic properties and stability criteria of zeros of sampled data models for decouplable mimo systems this note analyzes the zeros of the sampled data models corresponding to continuous time decouplable mimo systems with all relative degrees less than or equal to two and shows approximate expressions of the zeros as power series expansions with respect to a sampling period further stability criteria of the zeros for small sampling periods are given

a method for the complete qualitative analysis of two coupled ordinary differential equations dependent on three parameters in this paper recent advances in bifurcation theory are specialized to systems describable by two coupled ordinary differential equations odes containing at most three independent parameters for such systems by plotting in the relevant parameter plane the locus of successively degenerate singular points a complete description of all the qualitatively distinct behaviour of the system can be obtained the description is in terms of phase portraits and bifurcation diagrams even though much use is made of existing results obtained via local analyses the results of this technique cover the entire parameter space furthermore because the information is built up in successive stages the question of whether the parameters universally unfold a given degeneracy does not arise this can mean a major saving in effort particularly for degenerate hopf points finally if as is often the case the parameters appear in the system in a simple way the procedure can be applied analytically because the variables which will appear nonlinearly can be used to parametrize the relevant loci

limiting zeros of decouplable mimo systems for sufficiently rapid zero order hold zoh sampling it is known that the zeros of single input single output discrete time systems expressed in the forward shift operator converge to values determined only by the degrees of the finite and infinite zeros of the underlying continuous time system in this paper it is shown how this result can be generalized to multi input multi output mimo systems decouplable by static state feedback equivalently having a diagonal interactor matrix in the fast sampling limit the authors show how invariant and infinite zero structure is mapped under zoh sampling for discrete time systems expressed in either the delta forward difference or forward shift operators

an asymptotic analysis of the sal nikov thermokinetic oscillator the sal nikov thermokinetic oscillator is studied in the limiting case where the dimensionless heat capacity tends to zero this is equivalent to the no fuel consumption approximation in classical thermal explosion theory and is equally revealing in that many exact results can be obtained by simple algebraic methods regions in parameter space are found where although the system is asymptotically stable a large single excursion occurs before the steady state is approached these regions border the region of oscillations which in the limiting case are of the relaxation type all the interesting behaviour requires rt e frac 1 4 an obvious parallel with thermal explosion theory the unstable limit cycles that occur in the sal nikov oscillator disappear in this limiting case however the requirements for an unstable limit cycle to exist in the relaxation limit are discussed the homoclinic bifurcation in the limiting case is also examined and it is shown that this bifurcation can in theory be calculated exactly in addition an extension to the sal nikov oscillator scheme in a closed system to include fuel consumption is studied both numerically and in a limiting case it is shown that the full scheme exhibits finite trains of almost periodic behaviour before monotonically approaching equilibrium

on pairs of vectors achieving the maximal angle of a convex cone in this paper we explore the concept of antipodality relative to a closed convex cone the problem under consideration is that of finding a pair of unit vectors in k achieving the maximal angle of the cone we mention also a few words on the attainability of critical angles by way of application of the general theory we briefly discuss the problem of estimating the radius of pointedness of a cone

technical communique nyquist stability criterion of intrinsic zeros for continuous time pure imaginary zeros this note treats a stability condition of the zeros of sampled systems corresponding to continuous time pure imaginary zeros with multiplicity one for systems with the relative degree one it is shown that the nyquist plot can be used to check the stability condition

improvement of stability of zeros in discrete time multivariable systems using fractional order hold this paper is concerned with the stability of zeros of the discrete time multivariable systems composed of a fractional order hold froh a continuous time plant and a sampler in cascade the properties of the limiting zeros are studied and a condition for obtaining stable zeros for sufficiently small sampling periods is derived an approximate fractional order hold afroh is proposed as an implementation of froh it is shown that the afroh as well as the froh can locate the zeros of discrete time multivariable systems inside the stable region and improve stability properties when the zero order hold zoh cannot experimental results of adaptive control with afroh demonstrate a significant improvement of control performance compared with the use of a zoh

on the stability of the feasible set in optimization problems this paper provides stability theorems for the feasible set of optimization problems posed in locally convex topological vector spaces the problems considered in this paper have an arbitrary number of inequality constraints and one constraint set different models are discussed depending on the properties of the constraint functions linear or not convex or not but at least lower semicontinuous and one closed constraint set but not necessarily convex the parameter space is formed by systems of the same type as the nominal one with the same space of variables and the same number of constraints where the constraint set can be perturbed or not equipped with the metric of the uniform convergence on the positive multiples of a fixed barrelled neighborhood of zero in finite dimensions this topology describes the uniform convergence on compact sets and in the particular case that the constraints are linear the uniform convergence of the vector coefficients the paper examines in a unified way the lower and upper semicontinuity and the closedness of the feasible set mapping the stable consistency of the constraint system with respect to arbitrary and right hand side perturbations tuy and robinson regularities and other desirable stability properties of the feasible set