In this note, we consider a few important issues related to the maximization of the convergence rate inside a given ellipsoid for linear systems with input saturation. For continuous-time systems, the control that maximizes the convergence rate is simply a bang–bang control. Through studying the system under the maximal convergence control, we reveal several fundamental results on set invarianc...

Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first reduced the bang-bang control problem to finite-dimensional optimization and the...

A new fuzzy bang–bang relay controller (FBBRC) is introduced in this paper. The new controller is inherently optimal due to its bang–bang property. The controller has fuzzy decision-making capability in its inputs and have two fixed levels bang–bang output. Consequently, the tuning of FBBRC is restricted to input parameters only in comparison to standard fuzzy logic controller (FLC) where the o...

This paper presents the transient stability assessment of TCPST, UPFC and TCSC. The control laws based on few assumptions were applied and have been found to be effective for power oscillation damping for large and small signals. The bang-bang control strategy is used for IPFC in which the injected voltage magnitudes were kept constant and only one of voltage angles was varied. The results of t...

E.I.Verriest and F.L.Lewis have presented in [1] a new method to approach the minimum-time control of linear continous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost including time energy and precisions terms. Then, N.Elalami and N.Znaidi [2], extended these results to the discrete-time linear systems. The objective of this work is to propose an a...