48 research outputs found
Delay-dependent stability analysis for discrete-time systems with time varying state delay
The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results
Simple stability conditions of linear discrete time systems with multiple delay
In this paper we have established a new Lyapunov-Krasovskii method for linear discrete time systems with multiple time delay. Based on this method, two sufficient conditions for delay-independent asymptotic stability of the linear discrete time systems with multiple delays are derived in the shape of Lyapunov inequality. Numerical examples are presented to demonstrate the applicability of the present approach
Robust Stability of Singularly Impulsive Dynamical Systems
In this paper, we present results of the robust stability analysis for the class of nonlinear uncertain singularly impulsive dynamical systems. We present sufficient conditions for the robust stability of a class of nonlinear uncertain singularly impulsive dynamical systems. The problem of evaluating performance bounds for a nonlinear-nonquadratic hybrid cost functional depending upon a class of nonlinear uncertain singularly impulsive dynamical systems is considered. It turns out that the cost bound can be evaluated in closed form as long as the hybrid cost functional is related in a specific way to an underlying Lyapunov function that guarantees robust stability over a prescribed uncertainty set. Then, results for the case of uncertain singularly impulsive dynamical systems are presented. The results obtained for the nonlinear case are further specialized to linear singularly impulsive dynamical systems
On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach
U ovom radu razmatra se jedno moguÄe reÅ”enje baziÄne nelinearne kvadratne matriÄne jednaÄine. To reÅ”enje ima krucijelni znaÄaj u formulisanju posebnog kriterijuma, zavisnog od iznosa Äisto vremenskog kaÅ”njenja, za stabilnost na konaÄnom vremenskom intervalu posebne klase sistema sa kaÅ”njenjem, opisane svojim matriÄnim modelom x(k+1)=A0(k) + A1x(k-h). U tom smislu izveden je i odgovarajuÄi kriterijum stabilnosti koji ukljuÄuje i iznos Äisto vremenskog kaÅ”njenja. Mimo toga, posebno je apostrofiran znaÄaj nelinearnog diskretnog matriÄnog polinoma u stabilnosti sistema. KoristeÄi matematiÄki formalizam, baziran na Traub-ovom i Bernuli-jevom algoritmu, zakljuÄeno je da sraÄunavanje dominantnog solventa matriÄnog polinoma, ne garantuje potrebnu konvergenciju u svim sluÄajevima, kao sto je sluÄaj u tradicionalnim numeriÄkim procedurama. U ovom radu, prezentuje se jedno posebno i jedno opste reÅ”enje, koje važi za sluÄaj kada se matriÄni polinom može prikazati u faktorizovanom obliku. NumeriÄkim primerom ilustrovana je opravdanost predložene procedure.In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1)=A0(k)+A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results
SINGULARLY IMPULSIVE DYNAMICAL SYSTEMS WITH TIME DELAY: MATHEMATICAL MODEL AND STABILITY
In this paper we introduce a new class of systems, the so-called singularly impulsive or generalized impulsive dynamical systems with time delay. Dynamics of these systems is characterized by a set of differential and difference equations with time delay, and by algebraic equations. They represent a class of hybrid systems where algebraic equations represent constraints that differential and difference equations with time delay need to satisfy. In this paper we present a model, assumptions about the model, and two classes of singularly impulsive dynamical systems with delay ā time-dependent and state-dependent. Further, we present the Lyapunov and asymptotic stability theorems for nonlinear time-dependent and state-dependent singularly impulsive dynamical systems with time delay
On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach
U ovom radu razmatra se jedno moguÄe reÅ”enje baziÄne nelinearne kvadratne matriÄne jednaÄine. To reÅ”enje ima krucijelni znaÄaj u formulisanju posebnog kriterijuma, zavisnog od iznosa Äisto vremenskog kaÅ”njenja, za stabilnost na konaÄnom vremenskom intervalu posebne klase sistema sa kaÅ”njenjem, opisane svojim matriÄnim modelom x(k+1)=A0(k) + A1x(k-h). U tom smislu izveden je i odgovarajuÄi kriterijum stabilnosti koji ukljuÄuje i iznos Äisto vremenskog kaÅ”njenja. Mimo toga, posebno je apostrofiran znaÄaj nelinearnog diskretnog matriÄnog polinoma u stabilnosti sistema. KoristeÄi matematiÄki formalizam, baziran na Traub-ovom i Bernuli-jevom algoritmu, zakljuÄeno je da sraÄunavanje dominantnog solventa matriÄnog polinoma, ne garantuje potrebnu konvergenciju u svim sluÄajevima, kao sto je sluÄaj u tradicionalnim numeriÄkim procedurama. U ovom radu, prezentuje se jedno posebno i jedno opste reÅ”enje, koje važi za sluÄaj kada se matriÄni polinom može prikazati u faktorizovanom obliku. NumeriÄkim primerom ilustrovana je opravdanost predložene procedure.In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1)=A0(k)+A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results
FINITE-TIME STABILITY ANALYSIS OF DISCRETE TIME-DELAY SYSTEMS USING DISCRETE CONVOLUTION OF DELAYED STATES
Finite-time stability for the linear discrete-time system with state delay was investigated in this article. Stability of the system was analyzed using both the Lyapunov-like approach and the discrete Jensenās inequality. A novel Lyapunov-like functional with a discrete convolution of delayed states was proposed and used for the derivation of the sufficient stability conditions of the investigated system. As a result, the novel stability conditions guarantee that the states of the systems do not exceed the predefined boundaries on a finite time interval. The proposed methodology was illustrated with a numerical example. A computer simulation was performed for the analysis of the dynamical behavior of this system
Further results on non - Lyapunov stability of the linear nonautonomous systems with delayed state
Ovaj rad predstavlja dalji rad na osnovnim rezultatima u oblasti ograniÄenog vremena i praktiÄne stabilnosti linearnih, kontinualnih stacionarnih, neautonomnih sistema sa kaÅ”njenjem. Izdvojeni su dovoljni uslovi ovog tipa stabilnosti za odreÄenju klasu sistema sa kaÅ”njenjem. .Paper extends some basic results from the area of finite time and practical stability to linear, continuous, time invariant nonautonomous time-delay systems. Sufficient conditions of this kind of stability, for particular class of time-delay systems are derived.