Necessary and Sufficient Conditions for the Stability of Fourth Order and Fifth Order Systems

This paper aims at the fourth order and fifth order continuous time systems, respectively, to explore the necessary and sufficient conditions to ensure exponential stability. The main theorem shows that the necessary and sufficient conditions are only simple algebraic inequalities related to the coefficients of the characteristic equation. In other words, the stability of the fourth order and fifth order systems can be quickly and easily determined. Finally, we will present several numerical simulations to illustrate the practicability and correctness of the main results. Yeong-Jeu Sun "Necessary and Sufficient Conditions for the Stability of Fourth-Order and Fifth-Order Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-1 , December 2021, URL: https://www.ijtsrd.com/papers/ijtsrd49118.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/49118/necessary-and-sufficient-conditions-for-the-stability-of-fourthorder-and-fifthorder-systems/yeongjeu-sun