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89 Chapter 4 Hybrid Systems with Impacts Introduction The present subject of investigations is the hybrid systems with impacts in which moments of change of the state of the “continuous” coordinates are not predetermined. I.e., the momentary perturbations causing the switch from a state of differential equations to a new state of differential equations are not regulated in the systems by some independent models of computations. Instead, the moments of impulses result unequivocally from the arrangements of the dynamical system with the impacts. These

63 Chapter 3 Stability of Hybrid Systems in a Metric Space Introduction More general hybrid systems (than the ones of two classes discussed in the previous chapters) consist of heterogeneous subsystems related by interconnection operators [1, 26, 25 etc.]. The concept of generalized time [28, 30] made it possible to unify many results in this field by considering a generalized hybrid system in a metric space [30]. In this chapter, following the concept of this book we will consider hybrid systems with weakly interacting subsystems that are described

Chapter 1 Stability of Hybrid Systems on Time Scale Introduction The classical theory of motion stability unites methods and approaches that allow one to analyze stability of the equilibrium state in a mathematical model or a real process. Such models are, as a rule, systems of ordinary differential equations or partial differential equations. There are a number of monographs and books, which discuss basic approaches to this problem. Chapter 1 provides some concepts from time-scale calculus applied to analyze stability of the DE-model of a hybrid

29 Chapter 2 Stability of Hybrid Systems with Aftereffect Introduction In this chapter, the main attention is focused on the stability analysis of a hybrid system under impulse perturbations in terms of the generalized direct Lyapunov method. The impulse system is a classical hybrid system consisting of a continuous and discrete component. The presence of aftereffect in such a system expands the scope of possible applications in the study of real-world phenomena. Section 2.1 considers statement of the problem of motion stability of a hybrid system with

References [1] AJZERMAN, M. A.-HANTMAKHER, F. R.: Absolute Stability of Regulation Systems. Izd. AN USSR, Moscow, 1963. [2] BARBASHIN, E. A.: Method of Lyapunov Functions. Nauka, Moscow, 1970. [3] BRANICKY, M. S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control 43 (1998), 32-45. [4] BRANICKY,M. S.: Stability of switched and hybrid systems, in: Proc. 33rd Conf. Decision and Control, Lake Buena Vista, FL, 1994, pp. 3498-3503. [5] GELIG, A. KH.-LEONOV, G. A.-YAKUBOVICH, V. A.: Stability of Nonlinear

References Alcorta-Garcia, E. and Frank, P. (1997). Deterministic nonlinear observer based approach to fault diagnosis: A survey, Control Engineering Practice 5(5): 663-670. Blanke, M., Kinnaert, M., Lunze, J., and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control, Springer, Berlin. Cocquempot, V., Mezyani, T., and Staroswiecki, M. (2004). Fault detection and isolation for hybrid systems using structured parity residuals, 5th Asian Control Conference, Melbourne, Australia, pp. 1204-1212. Ding, S. (2014). Data-driven Design of Fault Diagnosis and Fault

hybrid models of cyber-physical systems and their implementation into distributed control system”, SCYR , pp. 62–63, TU, 2017. [5] D. Vošček, “Implementation enhancement of hybrid systems modelling within distributed control system”, SCYR , pp. 126–127, TU, 2018. [6] Y. Yang and X. Zhou, “Cyber-physical systems modeling based on extended hybrid automata”, Computational and Information Sciences (ICCIS), Fifth International Conference, pp. 1871–1874, IEEE, 2013. [7] P. Collins and J. H. Van Schuppen, “Observability of piecewise-affine hybrid systems”, International

References Ames, A. and Sastry, S. (2005). A homology theory for hybrid systems: Hybrid homology, in M. Morari and L. Thiele (Eds.), Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, Vol. 3414, Springer-Verlag, Berlin/Heidelberg, pp. 86–102. Balluchi, A., Benvenuti, L. and Sangiovanni-Vincentelli, A. (2005). Hybrid systems in automotive electronics design, 44th IEEE Conference on Decision and Control & 2005/2005 European Control Conference, CDC-ECC ’05, Seville, Spain , pp. 5618–5623. Blanchini, F. and Miani, S. (2008). Set

References [1] Lazar, M., Heemels, W. P. M. H., Weiland S., and Bemporad, A., “Stabilizing Model Predictive Control of Hybrid Systems,” in IEEE Transactions on Automatic Control , vol. 51, no. 11, Nov. 2006, pp. 1813-1818. [2] Witulski, A. F., Hernandez, A. F., and Erickson, R. W., “Small signal equivalent circuit modeling of resonant converters,” in IEEE Transactions on Power Electronics , vol. 6, no. 1, Jan 1991, pp. 11-27. [3] Sun, J., and Grotstollen, H., “Averaged modeling and analysis of resonant converters,” Power Electronics Specialists Conference