Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization

In this paper, we study the problem of optimizing the stability of positive semi-Markov jump linear systems. We specifically consider the problem of tuning the coefficients of the system matrices for maximizing the exponential decay rate of the system under a budget-constraint. By using a result from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices, we show that the stability optimization problem reduces to a convex optimization problem under certain regularity conditions on the system matrices and the cost function. We illustrate the validity and effectiveness of the proposed results by using an example from the population biology

A direct computation of state deadbeat feedback gains

A method for computing a feedback gain that achieves state deadbeat control is given. From systems given in the staircase form, this method derives the deadbeat gain in a numerically reliable way. It is shown that the gain turns out to be LQ optimal for some weightings

A direct algorithm for state deadbeat control

The authors propose a novel method for computing state deadbeat feedback gains from systems given in the staircase form. The proposed method uses only manipulations of given matrices, and hence is more direct than the existing method, which requires orthogonal transformations repeatedly. It is shown that the obtained gain is linear quadratic optimal for some weighting matrices </p

A construction of multivariable MRACS with fixed compensator using coprime factorization approach

A multivariable model reference adaptive control system (MRACS) with a fixed compensator is proposed. First, a new two-degree-of-freedom (2DOF) compensator with disturbance estimator is derived. Using this structure, a multivariable MRACS with fixed compensator is constructed. Since the proposed method is based on the 2 DOF structure, the fixed compensator is chosen independently of specifications for reference commands. The boundedness of all signals in the closed-loop system and the convergence of the output error are proved. A design method of the fixed compensator for MRACS with low sensitivity is also given. Finally, numerical examples are illustrated in order to show the effectiveness of the proposed method </p

Parametrization of identity interactors and the discrete-time all-pass property

This paper gives a concise parametrization of all identity interactors of a discrete-time multivariable square system. This is performed by means of a state-space description computed from a given particular interactor of the system. The paper then proposes a selection of the parameter which leads to an all-pass closed-loop transfer matrix. This closed-loop system turns out to be equivalent to a certain LQ (linear quadratic) optimal feedback system. A numerical example is given to illustrate the results</p