Hybrid discrete-continuous systems with control: II. State space method

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• 作者：V. M. Marchenko (1)
  
  1. Belarus State University of Technology ; Minsk ; Belarus
  
• 刊名：Differential Equations
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：51
• 期：1
• 页码：54-68
• 全文大小：414 KB
• 参考文献：1. Marchenko, V.M., Hybrid Discrete-Continuous Systems: I. Representation of Solutions, / Differ. Uravn., 2014, vol. 50, no. 11, pp. 1527鈥?540.
  2. Marchenko, V.M., Hybrid Discrete-Continuous Systems: II. Controllability and Reachability, / Differ. Uravn., 2013, vol. 49, no. 1, pp. 111鈥?22.
  3. Marchenko, V.M., Observability of Hybrid Discrete-Continuous Systems, / Differ. Uravn., 2013, vol. 49, no. 11, pp. 1421鈥?435.
  4. De la Sen, M., The Reachability and Observability of Hybrid Multirate Sampling Linear Systems, / Comput. Math. Appl., 1996, vol. 3, no. 1, pp. 109鈥?22. CrossRef
  5. Tsypkin, Ya.Z., / Teoriya lineinykh impul鈥檚nykh sistem (Theory of Nonlinear Impulsive Systems), Moscow: Nauka, 1973.
  6. Halanay, A. and Wexler, D., / Kachestvennaya teoriya impul鈥檚nykh sistem (The Qualitative Theory of Systems with Impulse), Moscow: Mir, 1971.
  7. Kalman, R., Falb, P., and Arbib, M., / Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title / Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971.
  8. Mesarovic, M. and Takahara, Y., / General Systems Theory: Mathematical Foundations, New York-London: Academic Press, 1975. Translated under the title / Obshchaya teoriya sistem: matematicheskie osnovy, Moscow: Mir, 1978.
  9. Manitius, A., F-Controllability and Observability of Linear Retarded Systems, / Appl. Math. Optim., 1982, vol. 9, pp. 73鈥?5. CrossRef
  10. Marchenko, V.M., On the Controllability and Observability of Systems with Aftereffect, / Dokl. Akad. Nauk BSSR, 1981, vol. 25, no. 3, pp. 239鈥?42.
  11. Nerode, A., Linear Automaton Transformations, / Proc. Amer. Math. Soc., 1958, vol. 9 (4), pp. 541鈥?44. CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Difference and Functional Equations
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3083

文摘

For hybrid discrete-continuous linear nonstationary systems, we introduce the notion of an s-state by minimal information. This permits one to suggest a common approach to the statement of a controllability problem for such systems in the sense of controllability of their states. We construct dual observation systems and justify the principle of duality between controllability and observability problems. As an example, we study the solvability of the problem of a strict complete controllability for the case in which the discrete component of a state is described by a stationary equation.