Using the impulse response sequences of the CFDDE and the balanced model-reduction method, a delay-free discrete-time state-space model is constructed.
Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between terms in the Leibniz Newton formula into account.
In terms of Lyapunov's direct method, a delay-dependent stability criterion is then derived to guarantee the asymptotic stability of NMTD interconnected systems.
Next, in terms of Lyapunov׳s direct method, a delay-dependent stability criterion is derived to guarantee the exponential stability of the NMTD interconnected system.
Based on the free weighting matrix method, a delay-dependent sufficient condition is established to guarantee that the output of the neutral systems tracks the output of a given reference model well in the H∞ sense.
By choosing a new Lyapunov Krasovskii (L K) functional, and by modifying the adding a power integrator method, a delay-independent output feedback controller is designed such that the system is globally asymptotically stable.
Based on the Lyapunov method, a delay-dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities, which can be easily solved by efficient convex optimization algorithms.
Using the Lyapunov functional method and the free-weighting matrix method, a delay-dependent sufficient condition for the existence of a desired filter is presented in the form of linear matrix inequalities (LMIs).
Without using the free weighting matrices method, a delay-range-dependent condition is derived in terms of strict linear matrix inequality (LMI), which guarantees that the singular system is regular, impulse free and mean-square exponentially stable with an H∞ performance.
Using Lyapunov functional and free-weighting matrix method, a delay-dependent stability criterion is obtained and formulated in the form of linear matrix inequalities, which can easily be checked by utilizing Matlab linear matrix inequality toolbox.
In this paper, we apply a new method, a delayed matrix exponential, to study P-type and D-type learning laws for time-delay controlled systems to track the varying reference accurately by using a few iterations in a finite time interval.
