Collection Of Linear Time-invariant Systems Research Articles

Realization and identification of autonomous linear periodically time-varying systems

The subsampling of a linear periodically time-varying system results in a collection of linear time-invariant systems with common poles. This key fact, known as “lifting”, is used in a two-step realization method. The first step is the realization of the time-invariant dynamics (the lifted system). Computationally, this step is a rank-revealing factorization of a block-Hankel matrix. The second step derives a state space representation of the periodic time-varying system. It is shown that no extra computations are required in the second step. The computational complexity of the overall method is therefore equal to the complexity for the realization of the lifted system. A modification of the realization method is proposed, which makes the complexity independent of the parameter variation period. Replacing the rank-revealing factorization in the realization algorithm by structured low-rank approximation yields a maximum likelihood identification method. Existing methods for structured low-rank approximation are used to identify efficiently a linear periodically time-varying system. These methods can deal with missing data.

Optimal Static Output Feedback Simultaneous Regional Pole Placement

The problem of optimal simultaneous regional pole placement for a collection of linear time-invariant systems via a single static output feedback controller is considered. The cost function to be minimized is a weighted sum of quadratic performance indices of the systems. The constrained region for each system can be the intersection of several open half-planes and/or open disks. This problem cannot be solved by the linear matrix inequality (LMI) approach since it is a nonconvex optimization problem. Based on the barrier method, we instead solve an auxiliary minimization problem to obtain an approximate solution to the original constrained optimization problem. Moreover, solution algorithms are provided for finding the optimal solution. Furthermore, a necessary and sufficient condition for the existence of admissible solutions to the simultaneous regional pole placement problem is derived. Finally, two examples are given for illustration.

The problem of simultaneous H∞ control

This paper considers the problem of simultaneous H ∞ control of a finite collection of linear time-invariant systems via a nonlinear digital output feedback controller. The main result is given in terms of the existence of suitable solutions to Riccati algebraic equations and a dynamic programming equation.

Simultaneous H∞ control of a finite collection of linear plants with a single nonlinear digital controller

This paper considers the problem of simultaneous H ∞ control of a finite collection of linear time-invariant systems via a nonlinear digital output feedback controller. The main result is given in terms of the existence of suitable solutions to Riccati algebraic equations and a dynamic programming equation. Our main result shows that if the simultaneous H ∞ control problem for k linear time-invariant plants of orders n 1, n 2,…, n k can be solved, then this problem can be solved via a nonlinear time-invariant controller of order n≜n 1+n 2+⋯+n k .

A controller design algorithm for a finite number of linear systems

In this paper, an algorithm is presented for the simultaneous stabilization of a set of linear time invariant (LTI) single-input and multi-input systems. Using the notion of quadratic stabilizability, a simple construction of a stabilizing controller is obtained. The class of LTI system [xdot] = Ax + bu, where A belongs to a set {Aa}, is considered-It is shown that this class of system is simultaneously stabilizable if{Aa} is simultaneously transformable into controllable companion form. The modifications of these results are suggested to accommodate the perturbation of matrix b. We also characterize a class of systems that are simultaneously transformable into companion form. In addition to the above results, it has also been proved that a collection of LTI systems is stabilizable by a single controller if they are simultaneously transformable into Hessenberg form. This class of system is shown to be larger than the class of uncertain systems that satisfies matching conditions

Optimal simultaneous stabilization of linear single-input systems via linear state feedback control

Simultaneous stabilization of a collection of linear time-invariant systems is considered. The aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses. Hurwitz's necessary and sufficient conditions are used as the required set of constraints for simultaneous stability. For transient behaviour, we introduce the usual quadratic objective function as performance index for each system. Their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the Hurwitz stability constraints. A computational technique is proposed for solving this problem. The results obtained give good transient behaviour. For illustration, two numerical examples are solved.