Control Problems for Fixed Finite Time Interval Stability

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

The Stability of Linear Discrete Time Delay Systems over a Finite Time Interval: An Overview

This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov–like functions. The practical and attractive practical stability for discrete time delay systems has been investigate...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

Finite-Time Input-to-State Stability and Applications to Finite-Time Control Design

This paper extends the well-known concept, input-to-state stability (ISS), to finitetime control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), along with related concepts such as finite-time input-output stability and finite-time small-gain theorems, is discussed, and then is applied to both the finite-time stability analysis and the finite-time stabiliz...