In this case the best that, in the current state of the research, can be done is to assume the above matrix with eigenvalues in the positive half-plane for any value of its arguments, and adopt a particular technique called integral sliding mode. Generalization to nonsingular matrices seems ...
Also, shows a nonsingular matrix, and let be decomposed into the singular value subsets: such that Υm×m is a positive diagonal matrix. Now, if one defines , then following relation can be derived from (19): (21) (22) where in σ1(t)∈ Rn−m, σ1(t)∈ Rm, , , , , ,...
. . ik ∀r ≤ s (11) • Transformation matrix of the C trigger in the instalments output R: it is the F matrix such that R = FC (12) It must be F = I + G. Consequently F has elements all equal to uk on the main diagonal, all equal to ik above the main diagonal, all...
is arbitrary, except that T must be nonsingular. Now note that if a plant and model satisfy (5) and (6), then (15) must be satisfied, and that (16) is the required similarity transformation. Equations (3) and (4) will be referred to as the standard form for perfect model following...
a sliding surface must first be established to ensure the desired convergence property. Subsequently, an SMC is constructed to guide the system states towards the selected position, unaffected by uncertainty or disturbances. The underlying concept of SMC is to maintain the control signal on the slidi...
nonsingular real matrix P such that P −1 B 1 P = [ 0 b −b 0 ] (b ̸= 0). Let J 1 = P −1 B 1 P and J 2 = P −1 B 2 P. Then J 1 and J 2 are commutative. By simple calculation, J 2 has the below form: J 2 = [ 0 c −c 0 ] (c ̸= 0...
Finally, a numerical example illustrates the superiority of the proposed method. Keywords: fractional-order switched singular systems; input-output finite-time stability; linear matrix inequalities; Φ-dependent average dwell time1. Introduction Recently, fractional calculus has drawn a great deal of ...
Additionally, the power supply for various electronic boards must be derived from the main battery pack. Consequently, the power module of an EV necessitates a configuration that accommodates multiple DC voltage levels. The suggested approach involves the integration of a buck–boost converter with ...
In the formula, is the investment coefficient matrix. Under normal circumstances, the A and B arrays are constant. Therefore, the dynamic input-output economic system model is highly hypothetical. In practical applications, the departmental elements in the model can also be expanded to include vario...
The designed parameter matrix 𝑐𝛿cδ determines the rate of decay of the tracking error, and satisfies condition 𝑐𝛿𝑇=𝑐𝛿>0cδT=cδ>0. The aim is to have the error 𝑒𝛿eδ be as close to zero as possible. Taking the derivative of Equation (19), 𝜎˙𝛿=𝑐...