Planovi i programi fizičkog vaspitanja u procesu obuke u JNA u periodu od 1951. do 1992. godine

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An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

A canonical form for the inclusion principle of dynamic systems

10.1109/ICCA.2007.43768852007 IEEE International Conference on Control and Automation, ICCA2863-286

A nested decomposition algorithm for parallel computations of very large sparse systems

In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are provided for matrices as large as 250,000×250,000, and its performance is compared to other sparse decompositions. Applications to the parallel solution of sparse systems are discussed for a variety of engineering problems

Šiljak, “A decomposition-based control strategy for large, sparse dynamic systems,”Mathematical

We propose a new output control design for large, sparse dynamic systems. A graphtheoretic decomposition is used to cluster the states, inputs, and outputs, and to identify an appropriate bordered block diagonal structure for the gain matrix. The resulting control law can be easily implemented in a multiprocessor environment with a minimum of communication. A large-scale problem is considered to demonstrate the validity of the proposed approach