A method for simultaneous strong stabilization of linear time-varying systems

Sufficient conditions for stability of linear time-varying systems

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

This work is concerned with the assignment of a desired PD-eigenstructure for linear time-varying systems. Despite its well-known limitations, gain scheduling control appeared to be a focus of the research efforts. Scheduling of frozen-time, frozen-state controllers for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper we: 1) introduce a differential algebraic eigenvalue theory for linear time-varying systems; and 2) propose a PD-eigenstructure assignment scheme via a differential Sylvester equation and a command generator tracker (CGT) for linear time-varying systems. The PD-eigenstructure assignment is utilized as a regulator. A feedforward gain for tracking control is computed by using the command generator tracker. The whole design procedures of the proposed PD-eigenstructure assignment scheme are systematic in nature. The scheme could be used to determine the stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for the linear time-varying systems. A missile flight control application is presented to validate the proposed schemes.

This paper considers the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> stability of systems with a convolution operator in the forward loop and a time-varying gain in the feedback loop. A frequency-domain condition involving the frequency response of the forward loop and the Fourier coefficients of the time-varying gain of the feedback loop is presented. The paper also contains a somewhat more involved time-domain condition in terms of the open-loop weighting pattern.

This paper investigates the problem of parameter-dependent state feedback control of continuous-time systems in the context of finite time stability. The controller is designed in order to guarantee that the closed-loop system is finite time stable. The system is considered time varying with the parameters modeled within a unit simplex. The design conditions obtained by means of Lyapunov functions are expressed as linear matrix inequalities. The finite time stability is assessed by using homogeneous polynomially parameter-dependent state feedback gains with arbitrary degree g. LMI relaxations are proposed based on Pólya's theorem. A controller is obtained by the solution of a factibility problem and the effect of the relaxation procedures analyzed by an optimization problem. Numerical examples are provided.

In this paper we consider the input-output stability of feedback systems consisting of a continuous-time, linear, time-varying plant with a discrete time, linear time-varying controller. These results generalize some of the results of Chen and Francis (1991, 1995) where the plant is restricted to be time-invariant.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On stability of linear time-varying systems

Stabilization and robustness analysis for time-varying systems with time-varying delays using a sequential subpredictors approach

The authors previously (Proc. 1990 IEEE International Symp. on Circuits and Systems, p.1393, 1990) presented an exact eigenvalue theory for the characterization of stability for linear time-varying systems. In this paper they extend these results to include precise characterizations and criteria for the quality of stability for linear, time-varying systems. These results provide analysts and control designers with a variety of mathematical tools and procedures for ensuring that the transient response of a linear, time-varying system is well behaved in the sense of settling-time, overshoot, etc. An example is given to illustrate the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robustness properties for time invariant systems were first studied in the context of Youla parameterization by Vidyasagar and Kimura ([13], [12]). There, plants are given by co-prime factorizations and neighbourhoods of the plant are characterized in terms of perturbations of the numerator and denominator of a given co-prime factorization. In this paper we give a generalization of this result to the time-varying setting. Because the natural notions of numerator, denominator, poles, zeroes for time-invariant systems do not have an obvious (or in some cases any) meaning in the time-varying case, another formulation is useful. We use the framework described in [2], which allows us to give a purely operator-theoretic formulation of this problem, strongly related to that given for time-invariant systems in the fundamental paper of Georgiou and Smith ([1]). Our main result (Theorem 4.3) is strongly related to that of Shamma ([10]) on the necessary condition for the Small-Gain Theorem for time-varying systems and our proof can be adapted to give what seems to be a more transparent proof of that result.KeywordsRobust StabilizationProper RepresentationNest AlgebraLeft RepresentationTransparent ProofThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Linear, finite-dimensional, time-varying systems are studied. State variable representations of systems with a bounded-input, bounded-output stability property which are uniformly stabilizable and detectable are shown to have their associated homogeneous state-variable systems exponentially stable.

Simultaneous stabilization with near-optimal model reference tracking

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

In this paper, an iterative computational method is proposed to handle constrained nonlinear quadratic optimal control problems. with terminal state constraints, saturation state and saturation control variables constraints. The method is based on replacing the original constrained nonlinear optimal control problem by a sequence of constrained linear time-varying quadratic optimal control problems. To this end, an iterative technique is used to replace the original constrained nonlinear dynamic system by a sequence of constrained linear time-varying systems. Then each of constrained linear time-varying quadratic optimal control problems is approximated by a quadratic programming problem by parameterizing each of the state variable by a finite length Legendre polynomials with unknown parameters. To show the effectiveness of the proposed method, simulation results of a constrained nonlinear optimal control problem are presented.

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.