SigPro 2.0.3 How To Compute Them

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Therefore, much attention has been devoted to the study of various systems with uncertainties, and a great number of useful results have been reported in the literature on the issues of robust stability, robust.

Firstly, a new matrix inequality considering uncertainties is introduced and proved.

By means of it, a novel sufficient condition for robust stability and stabilization of a class of uncertain switched discrete-time systems is presented.

Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability and stabilization have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method, and inequality technology.

Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

The motivation for studying switched systems comes partly from the fact that switched systems and switched multicontroller systems have numerous applications in control of mechanical systems, process control, automotive industry, power systems, aircraft and traffic control, and many other fields.

An important qualitative property of switched system is stability 1 3.

The challenge of analyzing the stability of switched system lies partly in the fact that, even if the individual systems are stable, the switched system might be unstable.

Using a common quadratic Lyapunov function on all subsystems, the quadratic Lyapunov stability facilitates the analysis and synthesis of switched systems.

In 10, various algorithms both for stability and performance analysis of discrete-time piece-wise affine systems were presented.

SigPro 2.0.3 How To Compute Them

Different classes of Lyapunov functions were considered, and how to compute them through linear matrix inequalities was also shown.

Moreover, the tradeoff between the degree of conservativeness and computational requirements was discussed.

The problem of stability analysis and control synthesis of switched systems in the discrete-time domain was addressed in 11.

The approach followed in 11 looked at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration.

Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function.

These two conditions have been proved to be equivalent for stability analysis.

There are many methodologies and approaches developed in the switched systems theory: approaches of looking for an appropriate switching strategy to stabilize the system 4, dwell-time and average dwell-time approaches for stability analysis and stabilization problems 5, approaches of studying stability and control problems under a specific class of switching laws 1, or under arbitrary switching sequences 6, 9.

Reference 19 investigated the quadratic stability and linear state feedback and output feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of noncommensurate constant internal point delays.

The results were obtained based on Lyapunov stability analysis via appropriate Krasovskii-Lyapunov functionals, and the related stability study was performed to obtain both delay-independent and delay-dependent results.

The problem of fault estimation for a class of switched nonlinear systems of neutral type was considered in 20.

The problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching was investigated in 21.

A state feedback controller was proposed to guarantee exponential stability and reliability for switched neutral systems, and the dwelltime approach was utilized for the stability analysis and controller design.

The exponential stability for a class of nonlinear hybrid time-delay systems was addressed in 24.

The delay-dependent stability conditions were presented in terms of the solution of algebraic Riccati equations, which allows computing simultaneously the two bounds that characterize the stability rate of the solution.

On another research front line, it has been recognized that parameter uncertainties, which often occur in many physical processes, are main sources of instability and poor performance.

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