Abstract The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented.
Abstract This paper compares the equilibrium outcomes under simultaneous and sequential output setting in a mixed duopoly in a vertically differentiated market. When the timing of the output game is determined endogenously, it is shown that simultaneous play in the quality stage with the public firm acting as the high-quality producer and simultaneous play in the second period in the output stage turn out to be the unique subgame perfect Nash equilibrium, which contrasts with the endogenous timing in a purely private duopoly.
In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.
Abstract Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.
Abstract This paper studies the H∞ disturbance attenuation problem for index one descriptor systems using the theory of differential games. To solve this disturbance attenuation problem the problem is converted into a reduced ordinary zero-sum game. Within a linear quadratic setting the problem is solved for feedback information structure.
Abstract In this paper, the method of periodically pinning intermittent control is introduced to solve the problem of outer synchronization between two complex networks. Based on the Lyapunov stability theory, differential inequality method and adaptive technique, some simple synchronous criteria have been derived analytically. At last, both the theoretical and numerical analysis illustrate the effectiveness of the proposed control methodology. This method not only reduces the conservatism of control gain but also saves the cost of production.These advantages make this method having a large application scope in the real production process.