Analysis Of Discrete-time Linear Systems Research Articles

Robust H2 Analysis of Discrete-Time Linear Systems Characterized by Random Polytopes and Time-Varying Parameters

This paper deals with discrete-time linear stochastic systems characterized by random polytopes and time-varying parameters. Random polytopes and time-varying parameters are introduced so that they can represent a sort of temporal variations in the distributions of coefficient random matrices of the systems. An H2 norm is defined for associated stochastic systems, and H2 performance analysis is discussed. In particular, we derive a numerically tractable linear matrix inequality condition for such analysis, as an extension of our earlier results about H2 control for stochastic systems without random polytopes.

Stability and passivity analysis of discrete-time linear systems with time-varying delay

This paper focuses on the stability and passivity analysis for a class of discrete-time linear systems. A novel general free-matrix-based summation inequality is proposed, and two improved stability criteria in terms of linear matrix inequalities (LMIs) are derived by employing the new summation inequality. Furthermore, when an external disturbance appears, a sufficient condition is established to ensure the considered linear system to be passive. Three numerical examples are provided to demonstrate the improvement of the proposed method.

Necessary and sufficient conditions to stability of discrete-time delay systems

This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ℓ2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples.

Parameter-memorized Lyapunov functions for discrete-time systems with time-varying parametric uncertainties

In this paper, a novel parameter-memorized Lyapunov function is proposed for stability analysis of discrete-time linear systems with time-varying parametric uncertainties. The parameter-memorized Lyapunov function depends on the uncertain parameters with a memory of a certain interval. It is shown that the previous parameter-dependent Lyapunov function is a special memoryless case of the parameter-memorized Lyapunov function, and as a result, the parameter-memorized Lyapunov function approach leads to less conservative results. Furthermore, if the length of the interval for parameter memory is sufficiently long, a nonconservative stability analysis result can be achieved. Numerical examples are provided to evaluate the obtained theoretical results.

Robust Stability Analysis of Discrete-Time Linear Systems with Dynamics Determined by a Markov Process

In this paper, we deal with discrete-time linear stochastic systems whose state transition is described by a sequence of random matrices determined by a Markov process. For such systems, we first show a linear-matrix-inequality-based stability condition. The use of conditional expectation plays a key role in the derivation. Then, we assume that the systems are uncertain in the sense that they are described by a sequence of random polytopes determined by a Markov process (to which the actual underlying random matrix sequence should belong), and extend the result about the above uncertainty-free case toward robust stability analysis, which leads to our main result. To show the usefulness of the result, we apply it to the case with stochastic switched systems having uncertain coefficient matrices, and provide a numerical example.

Stability of Discrete-time Control Systems with Uniform and Logarithmic Quantizers

Abstract: This paper deals with stability analysis of discrete-time linear systems involving finite quantizers on the input of the controlled plant. Two kinds of quantization are analyzed: uniform and logarithmic. Through LMI-based conditions, an attractor of the state trajectories and a set of admissible initial conditions are determined. A method is proposed to compare the performances of the two kinds of quantization in terms of the dimensions of the attractor, considering a scenario of Networked Control Systems (NCS). Computational issues are discussed and a numerical example is presented to validate the work.

Stability Analysis of Discrete-Time Linear Systems with Unbounded Stochastic Delays

This paper investigates the stability of discrete-time linear systems with stochastic delays. We assume that delays are modeled as random variables, which take values in integers with a certain probability. For the scalar case, we provide an analytical bound on the probability to guarantee the stability of linear systems. In the vector case, we derive a linear matrix inequality condition to compute the probability for ensuring the stability of closed-loop systems. As a special case, we also determine the step size of gradient algorithms with stochastic delays in the unconstrained quadratic programming to guarantee convergence to the optimal solution. Numerical examples are provided to show the effectiveness of the proposed analysis techniques.

Data-based analysis of discrete-time linear systems in noisy environment: Controllability and observability

In this paper, a data-based method is developed for analyzing the controllability and observability of discrete-time linear systems in noisy environment. This method uses measured data to estimate the controllability matrix and the observability matrix without identifying system models. The unbiasedness and consistency of this estimate with measurement noise and system noise are proven, respectively. As the estimated error of system parameters will not accumulate in calculating the controllability matrix and observability matrix, this method has a higher precision than traditional methods, especially in high-dimensional state space. In the simulation, the advantages of the data-based method in accuracy and convergence are illustrated.